its deformation behaviour. The hardness tester forces small sphere, pyramid or cone into the surface of the metals by means of a known applied load, and the hardness number( Brinell or Vickers diamond pyramid) then obtained from the diameter of the impres Instability The hardness may be related to the yield or tensile trength of the metal, since during the indentation, the Nominal strain En material around the impression is plastically deformed to a certain percentage strain. The vickers hardness Figure 7.2 Considere's construction number(VPN) is defined as the load divided by the pyramidal area of the indentation, in kgf/mm, and is about three times the yield stress for materials which stress at that strain, i.e. do/dE= o. Alternatively, since do not work harden appreciably. The Brinell hardness ke"= a= do/de= nke- then e=n and necking number(BHN) is defined as the stress P/A, in kgf/mm occurs when the true strain equals the strain-hardening where P is the load and A the surface area of the exponent. The instability condition may also be spherical cap forming the indentation. Thus expressed in terms of the conventional(nominal strain) dl/o do l BHN=P/D2)(-(-(d/D)21 /2) dl/I where d and d are the indentation and indentor diam =+(1+En)=a eters respectively. For consistent results the ratio d/D (7.3) should be maintained constant and small. Under these conditions soft materials have similar values of BHN which allows the instability point to be located using and VPN. Hardness testing is of importance in both Considere's construction(see Figure 7. 2), by plotting control work and research, especially where informa the true stress against nominal strain and drawing the tion on brittle materials at elevated temperatures tangent to the curve from En=-I on the strain axis. required The point of contact is the instability stress and the tensile strength is a/(1+En) Tensile specimens can also give information on the 7. 1. 4 Impact testing pe of fracture exhibited. Usually in polycrystalline A material may have a high tensile strength and yet metals transgranular fractures occur (i.e. the fracture be unsuitable for shock loading conditions. To deter urface cuts through the grains )and the cup and cone mine this the impact resistance is usually measured by type of fracture is extremely common in really duc- means of the notched or un-notched Izod or Charpy tile metals such as copper. In this, the fracture starts impact test. In this test a load swings from a given at the centre of the necked portion of the test piece height to strike the specimen, and the energy dissi s measured. The test is parti xis, so forming the cup,, but then, as it nears the ularly useful in showing the decrease in ductility and outer surface, it turns into a ' by fracturing along impact strength of materials of bcc structure at mod surface at about 45 to the tensile axis. In detail erately low temperatures. For example, carbon steels the itself consists of many irregular surfaces at have a relatively high ductile-brittle transition tem- about 45to the tensile axis, which gives the fracture a perature(Figure 7. Ic)and, consequently, they may be fibrous appearance. Cleavage is also a fairly common sed with safety at sub-zero temperatures only if the type of transgranular fracture, particularly in materi- transition temperature is lowered by suitable alloy als of bcc structure when tested at low temperatures ons or by refining the grain size. No The fracture surface follows certain crystal planes (e.g. increasing importance is given to defining a fracture [100) planes), as is shown by the grains revealing toughness parameter K for an alloy, since many alloys large bright facets, but the surface also arpels where critical stress, propagate; K, defines the critical com- contain small cracks which, when subjected to some cleavage planes have been tom apart. Intercrystallir fractures sometimes occur, often without appreciable discussed more fully in Chapter 8 deformation. This type of fracture is usually caused by a brittle second phase precipitating out around the 7.1.5 Creep testing grain boundaries, as shown by copper containing bis muth or antimony Creep is defined as plastic flow under constant stress and although the majority of tests are carried out under 7.1.3 Indentation hardness testing constant load conditions, equipment is available for reducing the loading during the test to compensate The hardness of a metal defined as the resistance to for the small reduction in cross-section of the spec- penetration,gives a conveniently rapid indication of imen. At relatively high temperatures creep appears toMechanical behaviour of materials 199 / )l/ : .Instobility / ff'y i/strain -1 0 Nominal strain E n Figure 7.2 Considbre's construction. stress at that strain, i.e. do"/de -- o.. Alternatively, since ke" = o. = dot/de = nke "-I then e = n and necking occurs when the true strain equals the strain-hardening exponent. The instability condition may also be expressed in terms of the conventional (nominal strain) do. do. de,, de de,, de do. (dl/lo) do. 1 de,, dl/)i = de, l0 do -- ~(1 + e,,) : o. (7.3) den which allows the instability point to be located using Consid6re's construction (see Figure 7.2), by plotting the true stress against nominal strain and drawing the tangent to the curve from e,, = -1 on the strain axis. The point of contact is the instability stress and the tensile strength is o./(1 + e,, ). Tensile specimens can also give information on the type of fracture exhibited. Usually in polycrystalline metals transgranular fractures occur (i.e. the fracture surface cuts through the grains) and the 'cup and cone' type of fracture is extremely common in really duc￾tile metals such as copper. In this, the fracture starts at the centre of the necked portion of the test piece and at first grows roughly perpendicular to the tensile axis, so forming the 'cup', but then, as it nears the outer surface, it turns into a 'cone' by fracturing along a surface at about 45 ~ to the tensile axis. In detail the 'cup' itself consists of many irregular surfaces at about 45 ~ to the tensile axis, which gives the fracture a fibrous appearance. Cleavage is also a fairly common type of transgranular fracture, particularly in materi￾als of bcc structure when tested at low temperatures. The fracture surface follows certain crystal planes (e.g. {100} planes), as is shown by the grains revealing large bright facets, but the surface also appears gran￾ular with 'river lines' running across the facets where cleavage planes have been torn apart. Intercrystalline fractures sometimes occur, often without appreciable deformation. This type of fracture is usually caused by a brittle second phase precipitating out around the grain boundaries, as shown by copper containing bis￾muth or antimony. 7.1.3 Indentation hardness testing The hardness of a metal, defined as the resistance to penetration, gives a conveniently rapid indication of its deformation behaviour. The hardness tester forces a small sphere, pyramid or cone into the surface of the metals by means of a known applied load, and the hardness number (Brinell or Vickers diamond pyramid) is then obtained from the diameter of the impression. The hardness may be related to the yield or tensile strength of the metal, since during the indentation, the material around the impression is plastically deformed to a certain percentage strain. The Vickers hardness number (VPN) is defined as the load divided by the pyramidal area of the indentation, in kgf/mm 2, and is about three times the yield stress for materials which do not work harden appreciably. The Brinell hardness number (BHN) is defined as the stress P/A, in kgf/mm 2 where P is the load and A the surface area of the spherical cap forming the indentation. Thus BUN --- P/(---~D2)2 / {1 -[1 -(d/O)2] '/2} where d and D are the indentation and indentor diam￾eters respectively. For consistent results the ratio diD should be maintained constant and small. Under these conditions soft materials have similar values of B HN and VPN. Hardness testing is of importance in both control work and research, especially where informa￾tion on brittle materials at elevated temperatures is required. 7.1.4 Impact testing A material may have a high tensile strength and yet be unsuitable for shock loading conditions. To deter￾mine this the impact resistance is usually measured by means of the notched or un-notched Izod or Charpy impact test. In this test a load swings from a given height to strike the specimen, and the energy dissi￾pated in the fracture is measured. The test is partic￾ularly useful in showing the decrease in ductility and impact strength of materials of bcc structure at mod￾erately low temperatures. For example, carbon steels have a relatively high ductile-brittle transition tem￾perature (Figure 7.1c) and, consequently, they may be used with safety at sub-zero temperatures only if the transition temperature is lowered by suitable alloy￾ing additions or by refining the grain size. Nowadays, increasing importance is given to defining a fracture toughness parameter Kc for an alloy, since many alloys contain small cracks which, when subjected to some critical stress, propagate; Kc defines the critical com￾bination of stress and crack length. Brittle fracture is discussed more fully in Chapter 8. 7.1.5 Creep testing Creep is defined as plastic flow under constant stress, and although the majority of tests are carded out under constant load conditions, equipment is available for reducing the loading during the test to compensate for the small reduction in cross-section of the spec￾imen. At relatively high temperatures creep appears to