Analysis of Distortion and Deformation Revised by Roch J. Shipley and David A Moore, Packer Engineering and William Dobson, Binary Engineering Associates. Inc Introduction THIS HANDBOOK is organized according to four general categories of failure: fracture, corrosion, wear, and the subject of this article, distortion. One reason metals are so widely used as engineering materials is that they have high strength but also generally have the capability to respond to load(stress) by deforming. In fact, much of metallurgical engineering is concerned with balancing strength and ductility. Thus, distortion often is observed in analysis of other types of failures, and consideration of the distortion can be an important part of the analysis. Energy is absorbed during deformation, and in some situations, the amount of energy absorbed may also be an important factor. Furthermore, it should be noted that not all distortion necessarily constitutes This article first considers true distortion failures that is situations in which distortion occurs when it should not have occurred and in which the distortion is associated with a functional failure. Then, a more general consideration of distortion in failure analysis is introduced. As used here, distortion will refer to a condition in which the shape of a component has changed without loss of material. Deformation will refer to the process that results in the distortion Distortion failure occurs when a structure or component is deformed so that it can no longer support the load was intended to carry, is incapable of performing its intended function, or interferes with the operation of another component. Distortion failures can be plastic or elastic and may or may not be accompanied by fracture. There are two main types of distortion: size distortion, which refers to a change in volume(growth or shrinkage), and shape distortion(bending or warping), which refers to a change in geometric form. Most of the examples in this article deal with metals, but the concepts also apply to nonmetals. Materials as diverse metals, polymers, and wood are all susceptible to distortion, although the mechanisms may differ somewhat among the different classes of material Distortion failures are ordinarily considered to be self-evident, for example, damage of a car body in a collision or bending of a nail being driven into hard wood. However, the failure analyst is often faced with more subtle situations. For example, the immediate cause of distortion(bending) of an automobile-engine valve stem is contact of the valve head with the piston, but the failure analyst must go beyond this immediate cause in order to recommend proper corrective measures. The valve may have stuck open because of faulty lubrication; the valve spring may have broken because corrosion had weakened it. The spring may have had insufficient strength and taken a set, allowing the valve to drop into the path of the piston, or the engine may have been raced beyond its revolutions per minute limit many times, causing coil clash and subsequent fatigue fracture of the spring. Without careful consideration of all the evidence, the failure analyst may overlook the true cause of a distortion failure. Several common aspects of failure by distortion are discussed in this article, and suitable examples of distortion failures are presented for illustration Analysis of Distortion and Deformation Revised by Roch ]. Shipley and David A. Moore, Packer Engineering and william Dobson, Binary Engineering Associates, Inc. Overloading Every structure has a load limit beyond which it is considered unsafe or unreliable. Applied loads that exceed this limit are known as overloads and sometimes result(depending on the factor of safety used in design)in distortion or fracture of Thefileisdownloadedfromwww.bzfxw.com
Analysis of Distortion and Deformation Revised by Roch J. Shipley and David A. Moore, Packer Engineering and William Dobson, Binary Engineering Associates, Inc. Introduction THIS HANDBOOK is organized according to four general categories of failure: fracture, corrosion, wear, and the subject of this article, distortion. One reason metals are so widely used as engineering materials is that they have high strength but also generally have the capability to respond to load (stress) by deforming. In fact, much of metallurgical engineering is concerned with balancing strength and ductility. Thus, distortion often is observed in analysis of other types of failures, and consideration of the distortion can be an important part of the analysis. Energy is absorbed during deformation, and in some situations, the amount of energy absorbed may also be an important factor. Furthermore, it should be noted that not all distortion necessarily constitutes a “failure.” This article first considers true distortion failures, that is, situations in which distortion occurs when it should not have occurred and in which the distortion is associated with a functional failure. Then, a more general consideration of distortion in failure analysis is introduced. As used here, distortion will refer to a condition in which the shape of a component has changed without loss of material. Deformation will refer to the process that results in the distortion. Distortion failure occurs when a structure or component is deformed so that it can no longer support the load it was intended to carry, is incapable of performing its intended function, or interferes with the operation of another component. Distortion failures can be plastic or elastic and may or may not be accompanied by fracture. There are two main types of distortion: size distortion, which refers to a change in volume (growth or shrinkage), and shape distortion (bending or warping), which refers to a change in geometric form. Most of the examples in this article deal with metals, but the concepts also apply to nonmetals. Materials as diverse as metals, polymers, and wood are all susceptible to distortion, although the mechanisms may differ somewhat among the different classes of material. Distortion failures are ordinarily considered to be self-evident, for example, damage of a car body in a collision or bending of a nail being driven into hard wood. However, the failure analyst is often faced with more subtle situations. For example, the immediate cause of distortion (bending) of an automobile-engine valve stem is contact of the valve head with the piston, but the failure analyst must go beyond this immediate cause in order to recommend proper corrective measures. The valve may have stuck open because of faulty lubrication; the valve spring may have broken because corrosion had weakened it. The spring may have had insufficient strength and taken a set, allowing the valve to drop into the path of the piston, or the engine may have been raced beyond its revolutions per minute limit many times, causing coil clash and subsequent fatigue fracture of the spring. Without careful consideration of all the evidence, the failure analyst may overlook the true cause of a distortion failure. Several common aspects of failure by distortion are discussed in this article, and suitable examples of distortion failures are presented for illustration. Analysis of Distortion and Deformation Revised by Roch J. Shipley and David A. Moore, Packer Engineering and William Dobson, Binary Engineering Associates, Inc. Overloading Every structure has a load limit beyond which it is considered unsafe or unreliable. Applied loads that exceed this limit are known as overloads and sometimes result (depending on the factor of safety used in design) in distortion or fracture of The file is downloaded from www.bzfxw.com
one or more structural members. Estimation of load limits is one of the most important aspects of design and is commonly computed by one of two methods--classical design or limit analysis Classical Design. The conservative, classical method of design(assuming monotonic or static loading) assumes that failure occurs whenever the stress at any point in a structure exceeds the yield strength of the material. Except for members that are loaded in pure tension, the fact that yielding occurs at some point in a structure has little influence on the ability of the structure to support the load. However, yielding has long his classical approach inherently assumes that or fracture and is therefore a reasonable basis for limiting applied loads the stress to cause fracture is greater than the stress to cause yield. As fracture mechanics analysis clearly shows, this may not be the case. Fracture may occur at loads less than that required to cause yield if a sufficiently large imperfection is present in the material Classical design keeps allowable stresses entirely within the elastic region and is used routinely in the design of parts Allowable stresses for static service are generally set at one-half the yield strength for ductile materials and one-sixth for brittle materials, although other fractions may be more suitable for specific applications. For very brittle materials, there may be little difference between the yield"and ultimate strength, and the latter is used in design computations. The reason for using such low fractions of yield (or ultimate) strength is to allow for such factors as possible errors computational assumptions, accidental overload, introduction of residual stress during processing, temperature effects, variations in material quality(including imperfections), degradation(for example, from corrosion), and inadvertent local increases in applied stress resulting from notch effects Classical design is also used for setting allowable stresses in other applications, for example, where fracture can occur by fatigue or stress rupture. In these instances, fatigue strength or stress-rupture strength is substituted for yield strength as a point of reference, typically with different factors of safety Limit Analysis. The upper limit in design is defined as the load at which a structure will break or collapse under a single application of force. This load can be calculated by a method known as limit analysis(Ref 1, 2). With limit analysis, it is unnecessary to estimate stress distributions, which makes stress analysis much simpler by this method than by classical design. However, limit analysis is based on the concept of tolerance to yielding in the most highly stressed regions of the structure and therefore cannot be used in designing for resistance to fatigue or elastic buckling or in designing flaw- tolerant structures Limit analysis assumes an idealized material-one that behaves elastically up to a certain yield strength, then does not work harden but undergoes an indefinite amount of plastic deformation with no change in stress. The inherent safety of a structure is more realistically estimated by limit analysis in those instances when the structure will tolerate some plastic deformation before it collapses. Because low-carbon steel, one of the most common materials used in structural members behaves somewhat like the idealized material, limit analysis is very useful to the designer, especially in the analysis of statically indeterminate structures Figure 1 illustrates the relative stress-strain behavior of a low-carbon steel, a strain-hardening material, and an idealized material-all with the same yield strength(the upper yield point for the low-carbon steel and the stress at 0. 2% offset for the strain-hardening material ) Load limits for parts made of materials that strain harden significantly when stressed in the plastic region can be estimated by limit analysis, as can those for parts made of other materials whose stress-strain behavior differs from that of the idealized material. In these situations the designer bases his design calculations on assumed strength that may actually lie well within the plastic region for the material Strain-hardening Low-carbon ste Idealized moterial Strain
one or more structural members. Estimation of load limits is one of the most important aspects of design and is commonly computed by one of two methods—classical design or limit analysis. Classical Design. The conservative, classical method of design (assuming monotonic or static loading) assumes that failure occurs whenever the stress at any point in a structure exceeds the yield strength of the material. Except for members that are loaded in pure tension, the fact that yielding occurs at some point in a structure has little influence on the ability of the structure to support the load. However, yielding has long been considered a prelude to structural collapse or fracture and is therefore a reasonable basis for limiting applied loads. This classical approach inherently assumes that the stress to cause fracture is greater than the stress to cause yield. As fracture mechanics analysis clearly shows, this may not be the case. Fracture may occur at loads less than that required to cause yield if a sufficiently large imperfection is present in the material. Classical design keeps allowable stresses entirely within the elastic region and is used routinely in the design of parts. Allowable stresses for static service are generally set at one-half the yield strength for ductile materials and one-sixth for brittle materials, although other fractions may be more suitable for specific applications. For very brittle materials, there may be little difference between the “yield” and ultimate strength, and the latter is used in design computations. The reason for using such low fractions of yield (or ultimate) strength is to allow for such factors as possible errors in computational assumptions, accidental overload, introduction of residual stress during processing, temperature effects, variations in material quality (including imperfections), degradation (for example, from corrosion), and inadvertent local increases in applied stress resulting from notch effects. Classical design is also used for setting allowable stresses in other applications, for example, where fracture can occur by fatigue or stress rupture. In these instances, fatigue strength or stress-rupture strength is substituted for yield strength as a point of reference, typically with different factors of safety. Limit Analysis. The upper limit in design is defined as the load at which a structure will break or collapse under a single application of force. This load can be calculated by a method known as limit analysis (Ref 1, 2). With limit analysis, it is unnecessary to estimate stress distributions, which makes stress analysis much simpler by this method than by classical design. However, limit analysis is based on the concept of tolerance to yielding in the most highly stressed regions of the structure and therefore cannot be used in designing for resistance to fatigue or elastic buckling or in designing flawtolerant structures. Limit analysis assumes an idealized material—one that behaves elastically up to a certain yield strength, then does not work harden but undergoes an indefinite amount of plastic deformation with no change in stress. The inherent safety of a structure is more realistically estimated by limit analysis in those instances when the structure will tolerate some plastic deformation before it collapses. Because low-carbon steel, one of the most common materials used in structural members, behaves somewhat like the idealized material, limit analysis is very useful to the designer, especially in the analysis of statically indeterminate structures. Figure 1 illustrates the relative stress-strain behavior of a low-carbon steel, a strain-hardening material, and an idealized material—all with the same yield strength (the upper yield point for the low-carbon steel and the stress at 0.2% offset for the strain-hardening material). Load limits for parts made of materials that strain harden significantly when stressed in the plastic region can be estimated by limit analysis, as can those for parts made of other materials whose stress-strain behavior differs from that of the idealized material. In these situations, the designer bases his design calculations on an assumed strength that may actually lie well within the plastic region for the material
Fig. 1 Comparison of the conventional stress-strain behavior of a low-carbon steel,a strain-hardening material, and the idealized material assumed in limit analysis. all have the same yield strength. Buckling Collapse due to instability under compressive stress, or buckling, may or may not be permanent deformation, depending on whether or not the yield strength was exceeded. Long, slender, straight bars, tubes, or columns under axial compressive forces will buckle when the buckling load is exceeded. Buckling failure may also be encountered on the compressive sides of tubes, I-beams, channels, and angles under bending forces. Tubes may also buckle due to torsional forces, causing waves, or folds, generally perpendicular to the direction of the compressive-stress component. Parts under bending load are also subject to buckling failures on the compressive(concave)side(Fig. 2) c Fig 2 Buckled flange(lower arrow) of an extruded aluminum section deliberately loaded with a lateral force(upper arrow). Source: Ref 3. The buckling load depends only on the dimensions of the part and the modulus of elasticity of the material. Therefore, buckling cannot be prevented by changing the strength or hardness of the metal. The modulus of elasticity of a given metal is affected only by temperature, increasing at lower temperature and decreasing at higher temperature. buckling can be prevented only by changing the size or shape of the part with respect to the load imposed on it( Ref 3) The failure analyst should be sensitive to situations in which buckling has occurred but may not be immediately apparent a beam in bending will be more susceptible to buckling on the compression side if it is relatively deep and narrow. A thin, circular shaft in torsion may buckle into a helical configuration when a critical moment is exceeded. Creep or distortion from other causes may change the dimensions of a structure so that it becomes susceptible to buckling. Further details can be found in references such as ref 4 Safety Factors. In both classical design and limit analysis, yielding is assumed to be the criterion for calculating safe loads on statically loaded structures. For a given design and applied load, the two methods differ in that the safety factor( the ratio of the theoretical capacity of a structural member to the maximum allowable load)is generally higher when calculated by limit analysis. For example, classical design limits the capacity of a rectangular beam to the bending Thefileisdownloadedfromwww.bzfxw.com
Fig. 1 Comparison of the conventional stress-strain behavior of a low-carbon steel, a strain-hardening material, and the idealized material assumed in limit analysis. All have the same yield strength. Buckling. Collapse due to instability under compressive stress, or buckling, may or may not be permanent deformation, depending on whether or not the yield strength was exceeded. Long, slender, straight bars, tubes, or columns under axial compressive forces will buckle when the buckling load is exceeded. Buckling failure may also be encountered on the compressive sides of tubes, I-beams, channels, and angles under bending forces. Tubes may also buckle due to torsional forces, causing waves, or folds, generally perpendicular to the direction of the compressive-stress component. Parts under bending load are also subject to buckling failures on the compressive (concave) side (Fig. 2). Fig. 2 Buckled flange (lower arrow) of an extruded aluminum section deliberately loaded with a lateral force (upper arrow). Source: Ref 3. The buckling load depends only on the dimensions of the part and the modulus of elasticity of the material. Therefore, buckling cannot be prevented by changing the strength or hardness of the metal. The modulus of elasticity of a given metal is affected only by temperature, increasing at lower temperature and decreasing at higher temperature. Buckling can be prevented only by changing the size or shape of the part with respect to the load imposed on it (Ref 3). The failure analyst should be sensitive to situations in which buckling has occurred but may not be immediately apparent. A beam in bending will be more susceptible to buckling on the compression side if it is relatively deep and narrow. A thin, circular shaft in torsion may buckle into a helical configuration when a critical moment is exceeded. Creep or distortion from other causes may change the dimensions of a structure so that it becomes susceptible to buckling. Further details can be found in references such as Ref 4. Safety Factors. In both classical design and limit analysis, yielding is assumed to be the criterion for calculating safe loads on statically loaded structures. For a given design and applied load, the two methods differ in that the safety factor (the ratio of the theoretical capacity of a structural member to the maximum allowable load) is generally higher when calculated by limit analysis. For example, classical design limits the capacity of a rectangular beam to the bending The file is downloaded from www.bzfxw.com
moment that will produce tensile yielding in the regions farthest from the neutral axis; limit analysis predicts that It is important that the designer be abling moment 1.5 times the limiting bending moment determined by classical design complete collapse will occur at a bend le to relate the actual behavior of a structure to its assumed behavior because. for a given applied load and selected safety factor, a structure designed by limit analysis will usually have thinner sections than a structure designed by classical methods Safety factors are important design considerations because they allow for factors that cannot be computed in advance Overload failure can occur either when the applied loads increase the stress above the design value or when the material strength is degraded. If either situation is a characteristic of the fabricated structure the design must be changed to allow for these factors more realistically Example 1: Collapse of Extension Ladders by Overloading of Side Rails. Several aluminum alloy extension ladders of the same size and type collapsed in service in the same manner; the extruded aluminum alloy 6063-T6 side rails buckled, but the rungs and hardware remained firmly in place. The ladders had a maximum extended length of 6.4 m(21 ft), and the recommended maximum angle of inclination to the vertical was 15 Ivestigation. Visual examination disclosed that the side-rail extrusions, which had the I-beam shape shown in Fig. 3(a) had failed by plastic buckling, with only slight surface cracking in the most severely deformed areas. There were no isible defects in materials or workmanship, and all dimensions of the side rails were within specified tolerances 0.875 0046 3 0.046 0.6|o 0. 124(typ) 500 卫-E2E×o 400 30 00300040005000600.070 (b) Extrusion thickness in Fig 3 Aluminum alloy 6063-t6 extension- ladder side-rail extrusion that failed by plastic deformation and subsequent buckling.(a) Configuration and dimensions(given in inches) (b) Relation of maximum applied load to the section thickness of the flanges and web of the side-rail extrusion Hardness tests using a portable hardness tester, metallographic examination, and tensile tests of specimens from the buckled side rails were conducted. All results agreed with the typical properties reported for aluminum alloy 6063-T6 extrusions Stress analysis of the design of the ladder, using actual dimensions, indicated that the side-rail extrusions had been designed with a thickness that would provide a safety factor of 1. 2 at ideal loading conditions(15 maximum inclination and that use of the ladders under other conditions could subject the side rails to stresses beyond the yield strength of the material Once yielding occurred, buckling would continue until the ladder collapsed The stress analysis was extended to include an evaluation of the relation of maximum applied load to section thickness ith the ladder at its maximum extension of 6.4 m(21 ft)and at an inclination of 15. This relation is shown in Fig 3 (b) Conclusions. The side rails of the ladders buckled when subjected to loads that produced stresses beyond the yield ength of the alloy Failure was by plastic deformation, with only slight tearing in the most severely deformed regions
moment that will produce tensile yielding in the regions farthest from the neutral axis; limit analysis predicts that complete collapse will occur at a bending moment 1.5 times the limiting bending moment determined by classical design. It is important that the designer be able to relate the actual behavior of a structure to its assumed behavior because, for a given applied load and selected safety factor, a structure designed by limit analysis will usually have thinner sections than a structure designed by classical methods. Safety factors are important design considerations because they allow for factors that cannot be computed in advance. Overload failure can occur either when the applied loads increase the stress above the design value or when the material strength is degraded. If either situation is a characteristic of the fabricated structure, the design must be changed to allow for these factors more realistically. Example 1: Collapse of Extension Ladders by Overloading of Side Rails. Several aluminum alloy extension ladders of the same size and type collapsed in service in the same manner; the extruded aluminum alloy 6063-T6 side rails buckled, but the rungs and hardware remained firmly in place. The ladders had a maximum extended length of 6.4 m (21 ft), and the recommended maximum angle of inclination to the vertical was 15°. Investigation. Visual examination disclosed that the side-rail extrusions, which had the I-beam shape shown in Fig. 3(a), had failed by plastic buckling, with only slight surface cracking in the most severely deformed areas. There were no visible defects in materials or workmanship, and all dimensions of the side rails were within specified tolerances. Fig. 3 Aluminum alloy 6063-T6 extension-ladder side-rail extrusion that failed by plastic deformation and subsequent buckling. (a) Configuration and dimensions (given in inches). (b) Relation of maximum applied load to the section thickness of the flanges and web of the side-rail extrusion. Hardness tests using a portable hardness tester, metallographic examination, and tensile tests of specimens from the buckled side rails were conducted. All results agreed with the typical properties reported for aluminum alloy 6063-T6 extrusions. Stress analysis of the design of the ladder, using actual dimensions, indicated that the side-rail extrusions had been designed with a thickness that would provide a safety factor of 1.2 at ideal loading conditions (15° maximum inclination) and that use of the ladders under other conditions could subject the side rails to stresses beyond the yield strength of the material. Once yielding occurred, buckling would continue until the ladder collapsed. The stress analysis was extended to include an evaluation of the relation of maximum applied load to section thickness with the ladder at its maximum extension of 6.4 m (21 ft) and at an inclination of 15°. This relation is shown in Fig. 3(b). Conclusions. The side rails of the ladders buckled when subjected to loads that produced stresses beyond the yield strength of the alloy. Failure was by plastic deformation, with only slight tearing in the most severely deformed regions
Corrective Measure. The flange and web of the side-rail extrusion were increased in thickness from 1. 2 to 1. 4 mm(0.046 to 0.057 in. ) This increased the safety factor from 1. 2 to 1.56. After this change, no further failures were reported. Note that this example is presented for illustrative purposes only, and this safety factor may not be appropriate in other applications Amount of Distortion. When designing structures using limit analysis, the designer does not al ways consider the amount of distortion that will be encountered. a rough illustration of the distortion that resulted from overloading of small cantilever beams is given in Fig. 4. Known loads were applied to rectangular-section beams of low-carbon steel and of stainless steel, and the permanent deflection at the loading point was measured. Maximum fiber stresses were calculated from the applied load and original specimen dimensions 2.50 Type 302 stainless steel, quarter hard Tensile strength, 135, 000 pal 200 1.75 |50 lolO steel(annealed) ield strength, 26, 000 psi ensile strength, 32 000 pal 1.0o 0.75 Distortion ratio Fig. 4 Relation of distortion ratio to stress ratio for two steel cantilever beams of rectangular cross section. Distortion ratio is permanent deflection, measured at a distance from the support ten times the beam thickness, divided by beam thickness. Stress ratio is maximum stress, calculated from applied load and original beam dimensions, divided by yield strength. This type of test provides a simplistic but useful concept of distortion by showing how much distortion occurs at strains beyond the yield point. As shown in Fig. 4, the beam of low-carbon steel, which strain hardens only slightly, exhibited no distortion when the calculated maximum fiber stress was equal to the yield strength(at a stress ratio of 1.00).However this beam collapsed at a load equivalent to a fiber stress just above the tensile strength, as shown in Fig 4 where the lower curve became essentially horizontal. This collapse load agrees with the limit-analysis collapse load of 1.5 times the load at yield. The beam made of stainless steel, which strain hardens at a rather high rate, showed no distortion at fiber stresses up to 1. 47 times the yield strength. When the calculated stress equaled the tensile strength(at a stress ratio of 1.59), distortion was 0.7 times the beam thickness, and the beam supported a calculated stress of 1.5 times the tensile strength without collapse It should be noted that the preceding example is intended simply to illustrate the differences in deformation behavior between two different materials. As a practical matter, one would not substitute stainless steel for low-carbon steel to increase load capacity. One would use a heavier section, or perhaps, a higher-strength alloy When loads increase gradually, distortion is gradual, and design can be based on knowledge of the amount of distortion that can be tolerated. Thus, simple bench tests of full-size or scaled-down models can often be used in estimating the loads required to produce various amounts of distortion Effect of Impact/Very High Strain Rates. When rapid or impulse loads are applied, as in impact, shock loading, or high- frequency vibration, the amount of distortion that can occur without fracture is considerably less predictable. The crystallographic processes involved in deformation and fracture are influenced by strain rate as well as temperature. For most structural materials, measured values of strength are higher under impulse loading, and values of ductility are lower, than the values measured under static loading. Tensile and yield strengths as much as 20% higher than the slow-tension test values have been measured under very high rates of loading. Strain-rate sensitivity data have been compiled for many Thefileisdownloadedfromwww.bzfxw.com
Corrective Measure. The flange and web of the side-rail extrusion were increased in thickness from 1.2 to 1.4 mm (0.046 to 0.057 in.). This increased the safety factor from 1.2 to 1.56. After this change, no further failures were reported. Note that this example is presented for illustrative purposes only, and this safety factor may not be appropriate in other applications. Amount of Distortion. When designing structures using limit analysis, the designer does not always consider the amount of distortion that will be encountered. A rough illustration of the distortion that resulted from overloading of small cantilever beams is given in Fig. 4. Known loads were applied to rectangular-section beams of low-carbon steel and of stainless steel, and the permanent deflection at the loading point was measured. Maximum fiber stresses were calculated from the applied load and original specimen dimensions. Fig. 4 Relation of distortion ratio to stress ratio for two steel cantilever beams of rectangular cross section. Distortion ratio is permanent deflection, measured at a distance from the support ten times the beam thickness, divided by beam thickness. Stress ratio is maximum stress, calculated from applied load and original beam dimensions, divided by yield strength. This type of test provides a simplistic but useful concept of distortion by showing how much distortion occurs at strains beyond the yield point. As shown in Fig. 4, the beam of low-carbon steel, which strain hardens only slightly, exhibited no distortion when the calculated maximum fiber stress was equal to the yield strength (at a stress ratio of 1.00). However, this beam collapsed at a load equivalent to a fiber stress just above the tensile strength, as shown in Fig. 4 where the lower curve became essentially horizontal. This collapse load agrees with the limit-analysis collapse load of 1.5 times the load at yield. The beam made of stainless steel, which strain hardens at a rather high rate, showed no distortion at fiber stresses up to 1.47 times the yield strength. When the calculated stress equaled the tensile strength (at a stress ratio of 1.59), distortion was 0.7 times the beam thickness, and the beam supported a calculated stress of 1.5 times the tensile strength without collapse. It should be noted that the preceding example is intended simply to illustrate the differences in deformation behavior between two different materials. As a practical matter, one would not substitute stainless steel for low-carbon steel to increase load capacity. One would use a heavier section, or perhaps, a higher-strength alloy. When loads increase gradually, distortion is gradual, and design can be based on knowledge of the amount of distortion that can be tolerated. Thus, simple bench tests of full-size or scaled-down models can often be used in estimating the loads required to produce various amounts of distortion. Effect of Impact/Very High Strain Rates. When rapid or impulse loads are applied, as in impact, shock loading, or highfrequency vibration, the amount of distortion that can occur without fracture is considerably less predictable. The crystallographic processes involved in deformation and fracture are influenced by strain rate as well as temperature. For most structural materials, measured values of strength are higher under impulse loading, and values of ductility are lower, than the values measured under static loading. Tensile and yield strengths as much as 20% higher than the slow-tensiontest values have been measured under very high rates of loading. Strain-rate sensitivity data have been compiled for many The file is downloaded from www.bzfxw.com
materials and is important in analysis of manufacturing operations involving deformation(see, for example, Forming and Forging, Volume 14, ASM Handbook). The amount of distortion that can occur at high rates of loading is difficult to analyze or predict precisely because The variation, or scatter, among replicate tests of mechanical properties is greater when strain rates are high than it is when strain rates are low Impulse or impact loading involves the propagation of high-velocity stress waves through the structure, which may not be well quantified, with the most extreme example being ballistic impact with strain rates on the order of 10/min Impulse loading creates an adiabatic condition that causes a local increase in temperature Effect of Temperature. Distortion failures caused by overload can occur at any temperature at which the flow strength of the material is less than the fracture strength. In this discussion, flow strength is defined as the average true stress required to produce detectable plastic deformation caused by a relatively slow, continuously increasing application of load fracture strength is the average true stress at fracture caused by a relatively slow, continuously increasing application of load. The flow strength and fracture strength of a material are temperature dependent, as is the elastic modulus(Youngs modulus, bulk modulus, or shear modulus) Figure 5 illustrates this temperature dependence schematically for polycrystalline materials that do not undergo a solid- state transformation. Two flow strengths are shown: one for a material that does not have a ductile-to-brittle transition in fracture behavior, such as metal with a face-centered cubic(fcc)crystal structure, and one for a body-centered cubic(bcc) material that exhibits a ductile-to-brittle transition modulus Fracture strength Ow a strength(bcc materials) F strength(fcc materials) Homologous temperature Fig 5 Diagram of the temperature dependence of elastic plastic, and fracture behavior of polycrystalline materials that do not exhibit a solid-state transformation. bcc, body- centered cubic; fcc, face-centered cubic; T, instantaneous absolute temperature; TM, absolute melting temperature of the material As shown in Fig. 5, the flow strength, fracture strength, and elastic modulus of a material generally decrease as temperature increases. If a structure can carry a certain load at 20C(70F), it can carry the same load without deforming at lower temperatures. Stressed members made of materials having a ductile-to-brittle fracture transition will sometimes fracture spontaneously if the temperature is lowered to a value below the transition temperature(e.g, see the article Overload Failures"in this volume) If the temperature is increased so that the flow strength becomes lower than the applied stress, a structure may deform pontaneously with no increase in load. a change in temperature may also cause an elastic-distortion failure because of a change in modulus, as might occur in a control device where accuracy depends on a predictable elastic deflection of a ontrol element or a sensing element. For most structural materials, the curve defining the temperature dependence of elastic and plastic properties is relatively flat at temperatures near 20C(70F). For steels, the modulus is slightly decreasing until temperatures of approximately 320 to 370C(600 to 700F), are reached, at which point modulus starts to decrease more rapidly
materials and is important in analysis of manufacturing operations involving deformation (see, for example, Forming and Forging, Volume 14, ASM Handbook). The amount of distortion that can occur at high rates of loading is difficult to analyze or predict precisely because: · The variation, or scatter, among replicate tests of mechanical properties is greater when strain rates are high than it is when strain rates are low. · Impulse or impact loading involves the propagation of high-velocity stress waves through the structure, which may not be well quantified, with the most extreme example being ballistic impact with strain rates on the order of 104 /min. · Impulse loading creates an adiabatic condition that causes a local increase in temperature. Effect of Temperature. Distortion failures caused by overload can occur at any temperature at which the flow strength of the material is less than the fracture strength. In this discussion, flow strength is defined as the average true stress required to produce detectable plastic deformation caused by a relatively slow, continuously increasing application of load; fracture strength is the average true stress at fracture caused by a relatively slow, continuously increasing application of load. The flow strength and fracture strength of a material are temperature dependent, as is the elastic modulus (Young's modulus, bulk modulus, or shear modulus). Figure 5 illustrates this temperature dependence schematically for polycrystalline materials that do not undergo a solidstate transformation. Two flow strengths are shown: one for a material that does not have a ductile-to-brittle transition in fracture behavior, such as metal with a face-centered cubic (fcc) crystal structure, and one for a body-centered cubic (bcc) material that exhibits a ductile-to-brittle transition. Fig. 5 Diagram of the temperature dependence of elastic, plastic, and fracture behavior of polycrystalline materials that do not exhibit a solid-state transformation. bcc, bodycentered cubic; fcc, face-centered cubic; T, instantaneous absolute temperature; TM, absolute melting temperature of the material As shown in Fig. 5, the flow strength, fracture strength, and elastic modulus of a material generally decrease as temperature increases. If a structure can carry a certain load at 20 °C (70 °F), it can carry the same load without deforming at lower temperatures. Stressed members made of materials having a ductile-to-brittle fracture transition will sometimes fracture spontaneously if the temperature is lowered to a value below the transition temperature (e.g., see the article “Overload Failures” in this Volume). If the temperature is increased so that the flow strength becomes lower than the applied stress, a structure may deform spontaneously with no increase in load. A change in temperature may also cause an elastic-distortion failure because of a change in modulus, as might occur in a control device where accuracy depends on a predictable elastic deflection of a control element or a sensing element. For most structural materials, the curve defining the temperature dependence of elastic and plastic properties is relatively flat at temperatures near 20 °C (70 °F). For steels, the modulus is slightly decreasing until temperatures of approximately 320 to 370 °C (600 to 700 °F), are reached, at which point modulus starts to decrease more rapidly
In fcc materials, and in bcc materials at temperatures above the transition temperature but at lower homologous temperatures(<0.3 TM), distortion(net section yielding) always accompanies overload fracture in sections that do not contain a severe stress raiser. At higher homologous temperature, an increase in temperature may cause a change from transgranular(TG)to intergranular (IG) fracture with a concurrent decrease in ductility. That is, there is a minimum ductility at elevated temperature(within the"creep"range)where the fracture mechanism changes from TG to IG fracture with a concurrent loss in ductility Creep, or time-dependent strain, is a relatively long-term phenomenon and can be distinguished from overload distortion by relating the length of time at temperature to the amount of distortion, as discussed in the article " Creep and Stress Rupture Failures"in this Volume. The specific mechanisms and associated kinetics of creep are temperature dependent While creep is sometimes considered to be limited to temperatures above one- half of the absolute melting point and is usually associated with an intergranular mechanism at those temperatures, it is important for the failure analyst to know that long-term creep deformation and even fracture can also occur at lower temperatures and via other mechanisms Changes in operating temperature can affect the properties of a structure in other ways. At temperatures higher than about 30 to 40% of TM depending on the alloy, microstructural changes may occur over time and degrade properties, allowing distortion and even fracture to occur. For example, if a martensitic steel is tempered at a given temperature and then encounters a higher temperature in service, yield strength and tensile strength will decrease because of overtempering Long-time exposure to moderately elevated temperatures may cause overaging in a precipitation-hardening alloy, with a corresponding loss in strength. It is well known to metallurgists that exposure to cryogenic temperatures may cause cracking in a martensitic steel due to the volume change accompany ing the transformation of retained austenite. What may not be as well appreciated is that even if cracking does not occur, the transformation may create a distortion failure due to dimensional growth or warpage in a close-tolerance assembly, such as a precision bearing When the temperature is changed, different coefficients of thermal expansion for different materials in a heterogeneous structure can cause interference between structural members(or can produce permanent distortion because of thermally induced stresses if the members are joined together). The failure analyst must understand the effect of temperature on properties of the specific materials involved when analyzing failures that have occurred at temperatures substantially above or below the design or fabrication temperature Effect of Stress Raisers and Complex Stress States. In sections that do contain stress raisers, net section yielding can still occur if the state of stress is plane stress; that is, one normal stress component is 0. If the stress raiser results in sufficient constraint to produce plane strain, then gross yielding and distortion will not be observed. However, localized distortion may accompany crack extension as the inherent ductility of the material manifests itself. At the microscale, the fracture may or may not show evidence of ductility. That is, the material may be microscale ductile or brittle. If it is microscale ductile, there may still be no evidence of ductility at the macroscale. In inherently brittle materials, where the fracture stress is equal to the flow stress, no gross or localized distortion accompanies fracture, as discussed further in the article Fractures Appearance and Mechanisms of Deformation and Fracture "in this Volume The yield stress is generally taken as the critical value at which plastic deformation initiates. In uniaxial tension, it is clear when the applied stress reaches the yield point. However, for more complex multiaxial stress states, the point at which yield is anticipated may not be as clear. Theories such as maximum shear stress, maximum distortion energy, and others are detailed in Ref 4 and may be applied by the failure analyst if there is uncertainty as to whether the stresses known to be applied were sufficient to cause the distortion observed References cited in this section J W. Jones, Limit Analysis, Mach. Des., Vol 45(No. 23 ), 20 Sept 1973, p 146-151 2. D. Goldner, Plastic Bending in Tubular Beams, Mach. Des., Vol 45(No. 24), 4 Oct 1973, p 152-155 3. D.J. Ulpi, Understanding How Components Fail, 2nd ed, ASM International, 1999, p 16-19 4. J.A. Collins, Failure of Materials in Mechanical Design, 2nd ed, wiley and Sons, 1993 Analysis of Distortion and Deformation Revised by Roch J. Shipley and David A Moore, Packer Engineering and William Dobson, Binary Engineering Associates, Inc. Inappropriate Specifications Thefileisdownloadedfromwww.bzfxw.com
In fcc materials, and in bcc materials at temperatures above the transition temperature but at lower homologous temperatures (<0.3 TM), distortion (net section yielding) always accompanies overload fracture in sections that do not contain a severe stress raiser. At higher homologous temperature, an increase in temperature may cause a change from transgranular (TG) to intergranular (IG) fracture with a concurrent decrease in ductility. That is, there is a minimum ductility at elevated temperature (within the “creep” range) where the fracture mechanism changes from TG to IG fracture with a concurrent loss in ductility. Creep, or time-dependent strain, is a relatively long-term phenomenon and can be distinguished from overload distortion by relating the length of time at temperature to the amount of distortion, as discussed in the article “Creep and Stress Rupture Failures” in this Volume. The specific mechanisms and associated kinetics of creep are temperature dependent. While creep is sometimes considered to be limited to temperatures above one-half of the absolute melting point and is usually associated with an intergranular mechanism at those temperatures, it is important for the failure analyst to know that long-term creep deformation and even fracture can also occur at lower temperatures and via other mechanisms. Changes in operating temperature can affect the properties of a structure in other ways. At temperatures higher than about 30 to 40% of TM depending on the alloy, microstructural changes may occur over time and degrade properties, allowing distortion and even fracture to occur. For example, if a martensitic steel is tempered at a given temperature and then encounters a higher temperature in service, yield strength and tensile strength will decrease because of overtempering. Long-time exposure to moderately elevated temperatures may cause overaging in a precipitation-hardening alloy, with a corresponding loss in strength. It is well known to metallurgists that exposure to cryogenic temperatures may cause cracking in a martensitic steel due to the volume change accompanying the transformation of retained austenite. What may not be as well appreciated is that even if cracking does not occur, the transformation may create a distortion failure due to dimensional growth or warpage in a close-tolerance assembly, such as a precision bearing. When the temperature is changed, different coefficients of thermal expansion for different materials in a heterogeneous structure can cause interference between structural members (or can produce permanent distortion because of thermally induced stresses if the members are joined together). The failure analyst must understand the effect of temperature on properties of the specific materials involved when analyzing failures that have occurred at temperatures substantially above or below the design or fabrication temperature. Effect of Stress Raisers and Complex Stress States. In sections that do contain stress raisers, net section yielding can still occur if the state of stress is plane stress; that is, one normal stress component is 0. If the stress raiser results in sufficient constraint to produce plane strain, then gross yielding and distortion will not be observed. However, localized distortion may accompany crack extension as the inherent ductility of the material manifests itself. At the microscale, the fracture may or may not show evidence of ductility. That is, the material may be microscale ductile or brittle. If it is microscale ductile, there may still be no evidence of ductility at the macroscale. In inherently brittle materials, where the fracture stress is equal to the flow stress, no gross or localized distortion accompanies fracture, as discussed further in the article “Fractures Appearance and Mechanisms of Deformation and Fracture” in this Volume. The yield stress is generally taken as the critical value at which plastic deformation initiates. In uniaxial tension, it is clear when the applied stress reaches the yield point. However, for more complex multiaxial stress states, the point at which yield is anticipated may not be as clear. Theories such as maximum shear stress, maximum distortion energy, and others are detailed in Ref 4 and may be applied by the failure analyst if there is uncertainty as to whether the stresses known to be applied were sufficient to cause the distortion observed. References cited in this section 1. J.W. Jones, Limit Analysis, Mach. Des., Vol 45 (No. 23), 20 Sept 1973, p 146–151 2. D. Goldner, Plastic Bending in Tubular Beams, Mach. Des., Vol 45 (No. 24), 4 Oct 1973, p 152–155 3. D.J. Wulpi, Understanding How Components Fail, 2nd ed., ASM International, 1999, p 16–19 4. J.A. Collins, Failure of Materials in Mechanical Design, 2nd ed., Wiley and Sons, 1993 Analysis of Distortion and Deformation Revised by Roch J. Shipley and David A. Moore, Packer Engineering and William Dobson, Binary Engineering Associates, Inc. Inappropriate Specifications The file is downloaded from www.bzfxw.com
Errors in specification of material or method of processing for a part can lead to distortion failures. These errors are often the result of faulty or incomplete information being available to the designer. In such instances, the designer has to make assumptions concerning the conditions of service Example 2: Distortion Failure of an Automotive Valve Spring. The engine of an automobile lost power and compression and emitted an uneven exhaust sound after several thousand miles of operation. When the engine was dismantled, it was found that the outer spring on one of the exhaust valves was too short to function properly. The short steel spring and an outer spring taken from another cylinder in the same engine(both shown in Fig. 6) were examined in the laboratory to determine why one had distorted and the other had not Fig. 6 Valve springs made from patented and drawn high-carbon steel wire. Distorted outer spring (left)exhibited about 25% set because of proeutectoid ferrite in the microstructure and high operating temperature Outer spring(right) is satisfactory. Investigation. The failed outer spring(at left, Fig. 6) had decreased in length to about the same free length as that of its companion inner spring. Most of the distortion had occurred in the first active coil (at top, Fig. 6), and a surface residue of baked-on oil present on this end of the spring indicated that a temperature of 175 to 205C (350 to 400F) had bec reached. Temperatures lower than 120C (250F)usually do not cause relaxation(or set)in high-carbon steel springs The load required to compress each outer spring to a length of 2.5 cm(1 in. ) was measured. The distorted spring needed only 30 kg(67 Ib), whereas the longer spring needed 41 kg(90 Ib). The distorted spring had suffered 25% set, which was the immediate cause of the engine malfunction The microstructure of both springs was primarily heavily cold-drawn fine pearlite, but the microstructure of the distorted spring contained small amounts of proeutectoid ferrite. Although the composition of the spring alloy was unknown, the microstructure indicated that the material was patented and cold-drawn high-carbon steel wire. The distorted spring had a hardness of 43 HRC, and the longer spring had a hardness of 46 HrC. both hardness and microstructure indicated that the material in the deformed spring had 10% lower yield strength than material in the undeformed spring. The estimates of yield strength were considered valid because of two factors: the accuracy of the hardness testing and characteristically consistent ratios of yield strength to tensile strength for the grades of steel commonly used in spring wire Conclusions. The engine malfunctioned because one of the exhaust-valve springs had taken a 25% set in service Relaxation in the spring material occurred because of the combined effect of improper microstructure(proeutectoid ferrite) plus a relatively high operating temperature. The undeformed spring exhibited little or no set because the tensile trength and corresponding yield strength of the material(estimated from hardness measurements) were about 10% higher than those of the material in the deformed spring Recommendations. a higher yield strength and a higher ratio of yield strength to tensile strength can be achieved in the springs by using quenched-and-tempered steel instead of patented and cold-drawn steel. An alternative would be to use a more expensive chromium-vanadium alloy steel instead of plain carbon steel; the chromium-vanadium steel should be quenched and tempered. Regardless of material or processing specifications, if springs are stressed close to the yield point of the material, close control of material and processing plus stringent inspection are needed to ensure satisfactory rformance Service conditions are sometimes changed, invalidating certain assumptions that were made when the part was originally designed. Such changes include an increase in operating temperature to one at which the material no longer has the required strength, an increase in the load rating of an associated component, which the user may interpret as an increase in the allowable load on the structure as a whole, and an arbitrary increase in applied load by the user on the assumption that the component has a high enough safety factor to accommodate the added load
Errors in specification of material or method of processing for a part can lead to distortion failures. These errors are often the result of faulty or incomplete information being available to the designer. In such instances, the designer has to make assumptions concerning the conditions of service. Example 2: Distortion Failure of an Automotive Valve Spring. The engine of an automobile lost power and compression and emitted an uneven exhaust sound after several thousand miles of operation. When the engine was dismantled, it was found that the outer spring on one of the exhaust valves was too short to function properly. The short steel spring and an outer spring taken from another cylinder in the same engine (both shown in Fig. 6) were examined in the laboratory to determine why one had distorted and the other had not. Fig. 6 Valve springs made from patented and drawn high-carbon steel wire. Distorted outer spring (left) exhibited about 25% set because of proeutectoid ferrite in the microstructure and high operating temperature. Outer spring (right) is satisfactory. Investigation. The failed outer spring (at left, Fig. 6) had decreased in length to about the same free length as that of its companion inner spring. Most of the distortion had occurred in the first active coil (at top, Fig. 6), and a surface residue of baked-on oil present on this end of the spring indicated that a temperature of 175 to 205 °C (350 to 400 °F) had been reached. Temperatures lower than 120 °C (250 °F) usually do not cause relaxation (or set) in high-carbon steel springs. The load required to compress each outer spring to a length of 2.5 cm (1 in.) was measured. The distorted spring needed only 30 kg (67 lb), whereas the longer spring needed 41 kg (90 lb). The distorted spring had suffered 25% set, which was the immediate cause of the engine malfunction. The microstructure of both springs was primarily heavily cold-drawn fine pearlite, but the microstructure of the distorted spring contained small amounts of proeutectoid ferrite. Although the composition of the spring alloy was unknown, the microstructure indicated that the material was patented and cold-drawn high-carbon steel wire. The distorted spring had a hardness of 43 HRC, and the longer spring had a hardness of 46 HRC. Both hardness and microstructure indicated that the material in the deformed spring had 10% lower yield strength than material in the undeformed spring. The estimates of yield strength were considered valid because of two factors: the accuracy of the hardness testing and characteristically consistent ratios of yield strength to tensile strength for the grades of steel commonly used in spring wire. Conclusions. The engine malfunctioned because one of the exhaust-valve springs had taken a 25% set in service. Relaxation in the spring material occurred because of the combined effect of improper microstructure (proeutectoid ferrite) plus a relatively high operating temperature. The undeformed spring exhibited little or no set because the tensile strength and corresponding yield strength of the material (estimated from hardness measurements) were about 10% higher than those of the material in the deformed spring. Recommendations. A higher yield strength and a higher ratio of yield strength to tensile strength can be achieved in the springs by using quenched-and-tempered steel instead of patented and cold-drawn steel. An alternative would be to use a more expensive chromium-vanadium alloy steel instead of plain carbon steel; the chromium-vanadium steel should be quenched and tempered. Regardless of material or processing specifications, if springs are stressed close to the yield point of the material, close control of material and processing plus stringent inspection are needed to ensure satisfactory performance. Service conditions are sometimes changed, invalidating certain assumptions that were made when the part was originally designed. Such changes include an increase in operating temperature to one at which the material no longer has the required strength, an increase in the load rating of an associated component, which the user may interpret as an increase in the allowable load on the structure as a whole, and an arbitrary increase in applied load by the user on the assumption that the component has a high enough safety factor to accommodate the added load
Example 3: Bulging of a Shotgun Barrel Caused by a Change from Lead Shot to Iron Shot. A standard commercial shotgun barrel fabricated from 1138 steel deformed during a test that was made with a new type of ammunition. Use of the new ammunition, which contained soft iron shot with a hardness of about 72 HB, was intended to reduce toxicity; the old ammunition had contained traditional lead shot with a hardness of 30 to 40 HB Investigation. The shotgun barrel was of uniform inside diameter from the breech to a point 7.5 cm(3 in. from the muzzle; at this point, the inside diameter began to decrease("Before test"curve, Fig. 7a). This taper, or integral choke which is intended to concentrate the shot pattern, ended about 3. 8 cm(1-in. )from the muzzle, and the final portion of the barrel had a relatively uniform inside diameter 0.720 0.7|5 Afte O.71o test s s.705 0.700 0695 Before 0690 0685 00.51.015202.53.03.54.0 Distance from muzzle, in (a) 0850 0845 0840 After 0.835 90830 B825 Before test 0820 0.8|5 08|o 0.5|.01.52.02.53.03.54.0 Distance from muzzle in Fig. 7 Comparison of longitudinal profiles of an 1138 steel shotgun barrel before and after testing. 1000 rounds of a new type of ammunition were fired in the test(a) Inside diameter. (b) Outside diameter After a test in which 1000 rounds of ammunition containing soft iron shot were fired. the shotgun barrel had a longitudinal profile of inside diameter as shown in the"After test "curve in Fig. 7(a). Comparison of this curve with the Thefileisdownloadedfromwww.bzfxw.com
Example 3: Bulging of a Shotgun Barrel Caused by a Change from Lead Shot to Iron Shot. A standard commercial shotgun barrel fabricated from 1138 steel deformed during a test that was made with a new type of ammunition. Use of the new ammunition, which contained soft iron shot with a hardness of about 72 HB, was intended to reduce toxicity; the old ammunition had contained traditional lead shot with a hardness of 30 to 40 HB. Investigation. The shotgun barrel was of uniform inside diameter from the breech to a point 7.5 cm (3 in.) from the muzzle; at this point, the inside diameter began to decrease (“Before test” curve, Fig. 7a). This taper, or integral choke, which is intended to concentrate the shot pattern, ended about 3.8 cm (1 1 2 in.) from the muzzle, and the final portion of the barrel had a relatively uniform inside diameter. Fig. 7 Comparison of longitudinal profiles of an 1138 steel shotgun barrel before and after testing. 1000 rounds of a new type of ammunition were fired in the test. (a) Inside diameter. (b) Outside diameter After a test in which 1000 rounds of ammunition containing soft iron shot were fired, the shotgun barrel had a longitudinal profile of inside diameter as shown in the “After test” curve in Fig. 7(a). Comparison of this curve with the The file is downloaded from www.bzfxw.com
profile before the test shows that the effect of firing soft iron shot was to deform the gun barrel so that the choke taper ras shifted toward the muzzle. After the test, there was a bulge on the outside surface of the barrel, shown in comparisor to the longitudinal profile of the outside diameter before the test in Fig. 7(b). Deformation of the barrel had been detected after the first 100 rounds of iron-shot ammunition had been fired, and the bulge grew progressively larger as the test ontinued Apparently, the bore of the failed barrel was not concentric with the outside surface, because the wall thickness at a given distance from the breech varied widely among different points around the circumference. For example, at a distance of 5 mm(0. 2 in. )from the muzzle, the wall thickness varied from 1. 3 to 2 mm(0.051 to 0.080 in The microstructure of the barrel material was a mixture of ferrite and coarse pearlite. The alloy had a hardness of 163 to 198 HB(converted from Vickers hardness measurements) Based on previous tests, in which the hoop stress in shotgun barrels had been measured when lead-shot ammunition was fired, the safety factor had been estimated at 2.0. In this instance, it was concluded that wall thickness variations reduced the safety factor to about 1.3 for lead-shot ammunition. Previous tests had also shown that lead shot deformed extensively by impact with the bore in the choke zone of this type of gun barrel Analysis. The major stresses in the choke zone are produced by impact of shot pellets against the bore. When lead shot is used, the lead absorbs a considerable amount of the impact energy as it deforms. Soft iron shot, on the other hand, is much harder than lead and does not deform significantly. More of the impact energy is absorbed by the barrel when iron shot is used, producing higher stresses In this instance, had the gun barrel been of more uniform wall thickness around its circumference, it might not have deformed. However. it was believed that conversion to iron-shot ammunition would increase stresses in the barrel enough to warrant an increase in the strength of this type of barrel Conclusions. The shotgun barrel deformed because a change to iron-shot ammunition increased stresses in the choke zone of the barrel. Bulging was enhanced by a lack of uniformity in wall thickness Recommendations. Three alternative solutions to this problem were proposed, all involving changes in specifications The barrel could be made of steel with a higher yield strength The barrel could be made with a greater and more uniform wall thickne An alternative nontoxic metal shot with a hardness of about 30 to 40 HB could be developed for use in the ammunition Analysis of Distortion and Deformation Revised by Roch J. Shipley and David A Moore, Packer Engineering and william Dobson, Binary Engineering Associates, Inc. Failure to Meet specifications Parts sometimes do not perform to expectations because the material or processing does not conform to requirements, leaving the part with insufficient strength. For instance, a part can be damaged by decarburization, as discussed here for a spiral power spring Figure 8 shows two spiral power springs that were designed to counterbalance a textile- machine beam. The spring at left in Fig. 8 was satisfactory and took a normal set when loaded to solid deflection in a presetting operation. The spring at right in Fig. 8, after having been intentionally overstressed in the same manner as the satisfactory spring, exhibited 15% less reaction force than was required at 180 angular deflection because it had taken a set that was 30 in excess of the normal set
profile before the test shows that the effect of firing soft iron shot was to deform the gun barrel so that the choke taper was shifted toward the muzzle. After the test, there was a bulge on the outside surface of the barrel, shown in comparison to the longitudinal profile of the outside diameter before the test in Fig. 7(b). Deformation of the barrel had been detected after the first 100 rounds of iron-shot ammunition had been fired, and the bulge grew progressively larger as the test continued. Apparently, the bore of the failed barrel was not concentric with the outside surface, because the wall thickness at a given distance from the breech varied widely among different points around the circumference. For example, at a distance of 5 mm (0.2 in.) from the muzzle, the wall thickness varied from 1.3 to 2 mm (0.051 to 0.080 in.). The microstructure of the barrel material was a mixture of ferrite and coarse pearlite. The alloy had a hardness of 163 to 198 HB (converted from Vickers hardness measurements). Based on previous tests, in which the hoop stress in shotgun barrels had been measured when lead-shot ammunition was fired, the safety factor had been estimated at 2.0. In this instance, it was concluded that wall thickness variations had reduced the safety factor to about 1.3 for lead-shot ammunition. Previous tests had also shown that lead shot was deformed extensively by impact with the bore in the choke zone of this type of gun barrel. Analysis. The major stresses in the choke zone are produced by impact of shot pellets against the bore. When lead shot is used, the lead absorbs a considerable amount of the impact energy as it deforms. Soft iron shot, on the other hand, is much harder than lead and does not deform significantly. More of the impact energy is absorbed by the barrel when iron shot is used, producing higher stresses. In this instance, had the gun barrel been of more uniform wall thickness around its circumference, it might not have deformed. However, it was believed that conversion to iron-shot ammunition would increase stresses in the barrel enough to warrant an increase in the strength of this type of barrel. Conclusions. The shotgun barrel deformed because a change to iron-shot ammunition increased stresses in the choke zone of the barrel. Bulging was enhanced by a lack of uniformity in wall thickness. Recommendations. Three alternative solutions to this problem were proposed, all involving changes in specifications: · The barrel could be made of steel with a higher yield strength. · The barrel could be made with a greater and more uniform wall thickness. · An alternative nontoxic metal shot with a hardness of about 30 to 40 HB could be developed for use in the ammunition. Analysis of Distortion and Deformation Revised by Roch J. Shipley and David A. Moore, Packer Engineering and William Dobson, Binary Engineering Associates, Inc. Failure to Meet Specifications Parts sometimes do not perform to expectations because the material or processing does not conform to requirements, leaving the part with insufficient strength. For instance, a part can be damaged by decarburization, as discussed here for a spiral power spring. Figure 8 shows two spiral power springs that were designed to counterbalance a textile-machine beam. The spring at left in Fig. 8 was satisfactory and took a normal set when loaded to solid deflection in a presetting operation. The spring at right in Fig. 8, after having been intentionally overstressed in the same manner as the satisfactory spring, exhibited 15% less reaction force than was required at 180° angular deflection because it had taken a set that was 30° in excess of the normal set
