Plastic strain accommodation

Thus, as indicated above, in the submicron-sized 3Y-TZP ceramic, the stress-induced cyclic hardening, due to transformation taking place, was higher than under static deformation. NanocrystaUine 3Y-TZP softened cyclically, due to the formation of a large number of microcracks. In the submicron structures, this observation basically reflects the effects of dislocations and dislocation-dislocation interactions. In the nanocrystalline 3Y-TZP ceramic, this greater ability to accommodate plastic strain is probably due to grain-boundary sliding, since in nanocrystalline structures dislocations cannot move, because shp distances are on an atomic scale (hke the dimensions of dislocations themselves). 

Flaws of the size estimated from equation (5.82) are the median, radial, and lateral cracks caused by indentation, and the questions are where and why do they nucleate in a noncrystalline material Examination of the deformed zone beneath an indent or an impact shows that a series of intersecting flow lines is produced. Plastic strain is concentrated on the flow lines while the material between them is only strained elastically. Median cracks arise from the need to accommodate strains at the intersections of flow lines in a way analogous to crack nucleation from dislocations on intersecting slip planes in fully crystalline materials. 

Plastic strain causes local discontinuity of the metal surfaces due to slip-step formation. The protective films cannot instantaneously accommodate these very high local strains and suffer local damage or even breakdown. Consequently, the local weakening or destruction of the barrier between the base metal and the solution favors local anodic and often cathodic reactions and the related damages to the base metal. This is... 

At low plastic strain amplitudes (ACp/ 2<2xl0 ), the deformation is mainly accommodated by the softer austenitic phase of the duplex alloy. Movement of the screw dislocations in the a-phase is very difficult because of the low temperature behavior of this phase at 300 K. Cyclic deformation of the austenitic phase then controls the fatigue properties of the duplex alloy. Because of the large reversibility of the cyclic strain, delayed transgranular crack initiation occurs in this phase (Fig. 5-34a). This explains the good fatigue resistance of the two-phase alloy at Agp/2< 10" as shown in the Coffin-Manson curve (Fig. 5-33). 

It is important to note that a major role of solder in area array solder joints at the chip and package level is to accommodate plastic strain without cracking that is, the solder is a plastic strain absorber. This implies that weak solders are potentially good candidates for this application. It has been demonstrated that solders with low shear strengths exhibit the greatest thermal cycling lifetimes [124], and this explains the lower thermal mechanical fatigue resistance of tin-based solders compared to lead-based solders (Table 5). 

We first consider strain localization as discussed in Section 6.1. The material deformation action is assumed to be confined to planes that are thin in comparison to their spacing d. Let the thickness of the deformation region be given by h then the amount of local plastic shear strain in the deformation is approximately Ji djh)y, where y is the macroscale plastic shear strain in the shock process. In a planar shock wave in materials of low strength y e, where e = 1 — Po/P is the volumetric strain. On the micromechanical scale y, is accommodated by the motion of dislocations, or y, bN v(z). The average separation of mobile dislocations is simply L = Every time a disloca-... 

Dislocations are commonly present in two regions. A layer with high mismatch may relax so that interface dislocations are created to accommodate the strain. A network at the interface is thns observed. Shp dislocations may be generated by local plastic deformation due to thermal or mechanical strain and propagate elsewhere in the layer. Dislocations in the layer itself may also be generated during the growth process, dne, for example, to the presence of inclusions. 

Plastic deformation (strain). When two surfaces of ductile materials are placed in contact and the load exceeds the elastic limit of one of the two materials, plastic deformation or strain occurs. The plastic deformation of one surface when two surfaces are in solid-state contact can occur in the presence or absence of lubricants. In fact, in some instances, the presence of lubricants can increase the deformability of the solid surfaces by a mechanism such as the Rehbinder effect. Plastic deformation of the solid surface is, therefore, observed in the presence of lubricants. Plastic deformation is accommodated by the generation of slip lines for dislocation flow in the solid surface. Dislocations are line defects in the solid and they are site of higher energy state on the surface. Thus, they interact or react more rapidly with certain chemical agents than do the bulk surfaces (Buckley, 1981 Lunarska and Samatowicz, 2000). 

Plastic deformation in crystalline solids occurs mostly as a result of dislocation motion and multiplication. Dislocations move on specific planes in certain directions when the applied stress exceeds the critical value of shear stress. In general, dislocations move with velocities that increase as the rate of deformation increases. However, due to the relativistic effect, dislocations are limited to move at velocities less than the shear wave velocity. Under high strain rate loading (10Vs-10 /s), dislocations accommodate this velocity restriction by high... 

When the blends are subjected to tensile testing, a certain fraction of the overall strain is accommodated by conservative deformation of the material. In the PP matrix, deformation results from the combination of amorphous phase hyperelasticity and crystal plasticity, as discussed earlier (50). The PA6 phase is also capable of deforming plastically, but its flow stress in the plastic stage is much higher than that of PP. Consequently, in the PP/PA6 blends the isolated PA6 particles exhibit less... 

Viscoelasticity is a very important behavior to understand for the designer. It is the relationship of stress with elastic strain in a plastic. The response to stress of all plastic structures is viscoelastic, meaning that it takes time for the strain to accommodate the applied stress field. Viscoelasticity can be viewed as a mechanical behavior in which the relationships between stress and strain are time dependent that may be extremely short or long, as opposed to the classical elastic behavior in which deformation and recovery both occur instantaneously on application and removal of stress, respectively (Figure 3.12). 

Moire interferometry is accomplished by first bonding a clear plastic film, marked with closely spaced lines, to the specimen. A second sheet, similarly marked, is then placed over the first but without bonding or electrostatic coupling. During incremental static loading, the bonded layer deforms while the second, unbonded layer, does not. Consequently, some lines will super-impose while others overlap (the so-called Moire effect). Lines of equal displacement appear which can be photographed or transformed to strains and stresses. The technique is inexpensive (less than 1000 for equipment and materials), but limited in application because significant curvature can not be accommodated. 

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