centre of an electric furnace heated by Sic elements 435 250 pe of the routine testing of graphite electrode samples and Carburized gives a useful indication of their ability to withstand accidental lateral impact during service in steel melting furnaces e Proof-testing is a long-established method of test g certain engineering components and structures In a typical proof test, each component is held at a Decarburized certain proof stress for a fixed period of time; load iron(0.004%C) ng and unloading conditions are standardized. In the ase of ceramics, it may involve bend-testing, inter- withstand the proof test are, in the simplest analysi udged to be sound and suitable for long-term service at the lower design stress. The underlying philosophy as been often questioned, not least because there is a Figure 7.5 S-N curve for carburized and decarburized iron risk that the proof test itself may cause incipient crack g. Nevertheless, proof-testing now has an important ole in the statistical control of strength in ceramics. 7.2 Elastic deformation 7. 2.1 Elastic deformation of metals 3 F(L-L It is well known that metals deform both elastically MoR= and plastically. Elastic deformation takes place at low stresses and has three main characteristics, namely 3-Point bend 4-Point b (1)it is reversible, (2)stress and strain are linearly proportional to each other according to Hooke's Law ons, MoR= modulus of and (3)it is usually small (i.e. <1%elastic strain) The stress at a point in a body is usually defined b=breadth of specimen, d by considering an infinitesimal cube surrounding that point and the forces applied to the faces of the cube by he surrounding material. These forces may be resolved known as the modulus of rupture(MoR)and expresses into components parallel to the cube edges and when the maximum tensile stress which develops on the con- divided by the area of a face give the nine stress vex face of the loaded beam. Strong ceramics, such as mponents shown in Figure 7.7. a given component silicon carbide and hot-pressed silicon nitride, have i is the force acting in the j-direction per unit ery high MoR values. The four-point loading method area of face normal to the i-direction. Clearly, when is often preferred because it subjects a greater volume i=j we have normal stress components(e.g.oux and area of the beam to stress and is therefore more which may be either tensile(conventionally positive) arching MoR values from four-point tests are often or compressive(negative), and when i+j(e.g oxy) substantially lower than those from three-point tests the stress components are shear. These shear stresses on the same material. Similarly, strength values tend exert couples on the cube and to prevent rotation of the to decrease as the specimen size is increased. To pro- cube the couples on opposite faces must balance and vide worthwhile data for quality control and design hence o =oi. Thus, stress has only six independent ctivities, close attention must be paid to strain rate components nd environment, and to the size, edge finish and sur. When a body is strained, small elements in that ace texture of the specimen. with oxide ceramics and body are displaced. If the initial position of an elem silica glasses, a high strain rate will give an appr iably higher flexural strength value than a low strain I'The nine components of stress ou form a second-rank rate, which leads to slow crack growth and delayed tensor usually written ction The bend test has also been adapted for use at high temperatures. In one industrial procedure, specimens of magnesia (basic) refractory are fed individually from a magazine into a three-point loading zone at the and is known as the stress tensorMechanical behaviour of materials 201 35 r- : 30 ,r￾x 25 ~ 20 15 Carburized i c' - C)~...... ~.004% Decarburized _ _ i _ i i ..... I I 104 I 0 S I 06 107 a 08 Cycles ~ N 250 200 E z if) L 150 m 100 Figure 7.5 S-N curve for carburized and decarburized iron. ~F ,,, [-i,- ....... a r~-/,,a d I , 2 2 3 FL MoR- 2 bd 2 I 32P0~nt bend I F F - | 2 2 3 F (L - L,) MoR= 2 bd 2 I 4iPo'nibend i Figure 7.6 Bend test configurations. MoR = modulus of rupture, F = applied force, L = outer span, Li = inner span, b = breadth of specimen, d = depth of specimen. known as the modulus of rupture (MoR) and expresses the maximum tensile stress which develops on the con￾vex face of the loaded beam. Strong ceramics, such as silicon carbide and hot-pressed silicon nitride, have very high MoR values. The four-point loading method is often preferred because it subjects a greater volume and area of the beam to stress and is therefore more searching. MoR values from four-point tests are often substantially lower than those from three-point tests on the same material. Similarly, strength values tend to decrease as the specimen size is increased. To pro￾vide worthwhile data for quality control and design activities, close attention must be paid to strain rate and environment, and to the size, edge finish and sur￾face texture of the specimen. With oxide ceramics and silica glasses, a high strain rate will give an appre￾ciably higher flexural strength value than a low strain rate, which leads to slow crack growth and delayed fracture (Section 10.7). The bend test has also been adapted for use at high temperatures. In one industrial procedure, specimens of magnesia (basic) refractory are fed individually from a magazine into a three-point loading zone at the centre of an electric furnace heated by SiC elements. A similar type of hot-bend test has been used for the routine testing of graphite electrode samples and gives a useful indication of their ability to withstand accidental lateral impact during service in steel melting furnaces. Proof-testing is a long-established method of test￾ing certain engineering components and structures. In a typical proof test, each component is held at a certain proof stress for a fixed period of time; load￾ing and unloading conditions are standardized. In the case of ceramics, it may involve bend-testing, inter￾nal pressurization (for tubes) or rotation at high speed ('overspeeding' of grinding wheels). Components that withstand the proof test are, in the simplest analysis, judged to be sound and suitable for long-term service at the lower design stress. The underlying philosophy has been often questioned, not least because there is a risk that the proof test itself may cause incipient crack￾ing. Nevertheless, proof-testing now has an important role in the statistical control of strength in ceramics. 7.2 Elastic deformation 7.2.1 Elastic deformation of metals It is well known that metals deform both elastically and plastically. Elastic deformation takes place at low stresses and has three main characteristics, namely (1) it is reversible, (2)stress and strain are linearly proportional to each other according to Hooke's Law and (3) it is usually small (i.e. <1% elastic strain). The stress at a point in a body is usually defined by considering an infinitesimal cube surrounding that point and the forces applied to the faces of the cube by the surrounding material. These forces may be resolved into components parallel to the cube edges and when divided by the area of a face give the nine stress components shown in Figure 7.7. A given component cr~j is the force acting in the j-direction per unit area of face normal to the /-direction. Clearly, when i = j we have normal stress components (e.g. crx~) which may be either tensile (conventionally positive) or compressive (negative), and when i ~ j (e.g. r the stress components are shear. These shear stresses exert couples on the cube and to prevent rotation of the cube the couples on opposite faces must balance and hence o" U = crji. 1 Thus, stress has only six independent components. When a body is strained, small elements in that body are displaced. If the initial position of an element 1The nine components of stress tTij form a second-rank tensor usually written tTxx O'x y tTx z tY y x tT y y tY y z tYzx tTzy tYZZ and is known as the stress tensor