Tensile stress plane

If a tensile load is applied to a material, the material will elongate on the axis of the load (perpendicular to the tensile stress plane), as illustrated in Figure 2(a). Conversely, if the load is compressive, the axial dimension will decrease, as illustrated in Figure 2(b). If volume is constant, a corresponding lateral contraction or expansion must occur. This lateral change will bear a fixed relationship to the axial strain. The relationship, or ratio, of lateral to axial strain is called Poisson s ratio after the name of its discoverer. It is usually symbolized by v. 

Mech nic lF tig ue. Some mechanical fatigue tests have been conducted on explosion-clad composites where the plane of maximum tensile stress is placed near the bond 2one (30). 

The condition for propagation of a mode 1 edge crack, that is, a crack that is subjected to pure opening (tensile) stresses appHed perpendicular to the crack plane, is given by (35) ... 

Romanchenko and Stepanov (1981) recognized that the impulse imparted at the spall plane to material downstream, because of the elastic-plastic nature of this material, led to an attenuating tensile stress pulse propagating toward the sample-window interface as is illustrated in Fig. 8.9. Thus, the maximum tension inferred from the measured spall signal should be adjusted for this attenuation in estimating a material spall strength at the spall plane. 

But we want the tensile yield strength, A tensile stress a creates a shear stress in the material that has a maximum value of t = a/2. (We show this in Chapter 11 where we resolve the tensile stress onto planes within the material.) To calculate cr from t,, we combine the Taylor factor with the resolution factor to give... 

Macrostrain is often observed in modified surfaces such as deposited thin films or corrosion layers. This results from compressive or tensile stress in the plane of the sample surface and causes shifts in diffraction peak positions. Such stresses can easily be analyzed by standard techniques if the surface layer is thick enough to detect a few diffraction peaks at high angles of incidence. If the film is too thin these techniques cannot be used and analysis can only be performed by assuming an un-... 

Linear elastic fracture mechanics (LEFM) is based on a mathematical description of the near crack tip stress field developed by Irwin [23]. Consider a crack in an infinite plate with crack length 2a and a remotely applied tensile stress acting perpendicular to the crack plane (mode I). Irwin expressed the near crack tip stress field as a series solution ... 

Rather than bearing an infinite stress at the crack tip, yielding occurs resulting in a volume of inelastically deformed material along the crack front called the process zone, as shown in Fig. 2. The size of the inelastic zone, r j , under a monotonic tensile stress, o , can be approximated by substituting o = Oj into eq. 2 for the horizontal plane, 0 = 0... 

The above discussion has assumed that the crack is loaded in mode 1 (the crack opening mode, with a tensile stress normal to the plane of the crack). Hydrogen has relatively little effect in modes II or III, as these generate shear stresses at the crack tip, rather than tensile stresses, and the shear behaviour of steels is relatively little affected by hydrogen, presumably because dilation of the lattice at the crack tip (which does not occur in modes II and III) is required for hydrogen accumulation. 

In the case of a thin sheet or film the stresses cause the material to be displaced completely away from the plane of the sheet and the restraint is by tensile stress in the sheet and by hoop stress around the puncturing member. Most cases fall somewhere between these extremes, but the most important conditions in practice involve the second condition to a larger degree than the first condition. 

Alle the deformation zones contain a finite and equal number of extended chains in their most highly stretched strands. This surprising conformity of the deformation zones may well be the consequence of the imposed plane-strain fracture condition which impedes lateral contraction of the material. However, no quantitative explanation has been presented as yet. A plausible explanation would be to assume that due to the hindered lateral contraction additional tensile stresses are transferred to the most extended strand with each additional chain pulled out of the matrix [112]. 

The more common type of spalling failure of concrete occurs when (and where) the transmitted compressive wave reflects from the free surface back face of the slab as a tensile wave, and the head of the reflected tensile wave and tail of the transmitted compressive wave combine to produce net tensile stress exceeding the dynamic tensile strength of the concrete. This process is shown schematically in Figure 21 for the simplified case of a plane, triangular compressive... 

The normal stress must be zero at the free surface, so a tension wave of a similar profile but opposite sign must start propagating in from the rear surfaces when the compressive front reaches this surface. The actual stress state shortly thereafter is shown in state 2 in Figure 21. When the tensile stress exceeds the tensile strength of the material, spall occurs on a plane parallel to the free surface. The normal stress then drops to zero again, and the process continues. In brittle materials weak in tension (such as concrete), it is possible for multiple spalls to occur before the reflected tensile waves decay enough to fall below the tensile strength. 

Lay up the reinforcements according to the stresses so that they really withstand the loads the planes of the reinforcements will be parallel to the tensile stresses, and perpendicular to the shear, flexural or compressive stresses. 

Fig. 1.14 One step in the movement of an edge dislocation through the crystal lattice. As a consequence of the extra-half plane of atoms regions are formed in the vicinity of dislocation where compressive and tensile stresses/strains are imposed on the neighboring atoms...

Consider a single crystal of BCC Mo oriented such that a tensile stress of 52 MPa is apphed along a [010] direction. From Table 5.1, we see that the slip plane for BCC Mo is (110) and the slip direction is [111]. 

Fig. 5.9 Ne field ion images of a GP[1] zone emerging from a (024) plane of an Al-4 wt% Cu alloy. This alloy was grown by Bridgeman method. After a homogenizing treatment at 793 K for 1.7 x lOf5 s, single crystal samples with a longer axis parallel to [001] were prepared. They were quenched into ice water and then aged at 403 K for 6 x 104 s under the tensile stress of 73.5 MPa along the [001]. Between a and b, 11 (024) layers were field evaporated, and between b and c, 16 more layers were evaporated. The distance between two Cu atoms should be 9.06 A as is shown in d. (Courtesy of M. Wada.)...

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