Compressive elastic stresses

When a foam is compressed, the stress-strain curve shows three regions (Fig. 25.9). At small strains the foam deforms in a linear-elastic way there is then a plateau of deformation at almost constant stress and finally there is a region of densification as the cell walls crush together. 

The strengthening effect of a monobloc cylinder due to autoffettage practically is achieved by two effects First the introduction of the compressive (tangential) residual stresses which extend the elastically admissible internal pressure and second the increased available material strength by strain hardening. The maximum admissible pressure for optimum autoffettaged cylinders based on perfectly elastic-plastic materials, completely elastic stress (plus/minus) conditions at the inner bore diameter and the assumption of the GE-hypothesis can be calculated as [11]. 

Compression tests, as well as tension tests, were carried out on the samples of varying AN content. All samples exhibited a compressive yield stress, and with further increase of strain, a subsequent drop in stress, occurred before the stress again started to rise. From the test data, the elastic modulus and the yield strength were determined as a function of nitrile content and the results are shown in Fig. 29. 

First, the elastic stress distributions of the un-notched specimens are obtained from a finite element analysis. For the PI un-notched specimen, the discrepancy between the finite element and the analytical result is very small (about 0.01%), thus validating the finite element calculation in terms of accuracy through the meshing and the type of element used. Therefore a similar calculation is conducted on the G1 un-notched specimen where the span to height ratio is smaller. The mismatch on the maximum stresses at the bottom and at the top of the beam between the finite element calculations and the analytical solution is 0.74% in tension and 0.79% in compression (and remains constant upon further mesh refinement). This estimation of the stress distribution is then used for the following evaluation of the stress intensity factor. 

Fig.5 shows the calculated curvature and temperature evolution for an FGM deposit with thickness of about 180 im, which is consistent with the experimental results shown in Fig.4 except for the transient oscillations. Fig.6 (a) shows the calculated stress distributions in 2-layer and FGM deposits. The gradual stress variation in the FGM can be observed. In Fig.6 (b) effects of model parameters such as the substrate temperature and elastic modulus of YPSZ on the stress distribution in 2-layer deposits are demonstrated. As the substrate temperature is raised from 600 to 825K, the tensile stress in the NiCrAlY layer is significantly reduced. If a value of elastic modulus of 190GPa of a dense bulk material was used, the compressive residual stress in the YPSZ is excessively overestimated. This example clearly demonstrates the importance of using realistic values for modeling thermal and mechanical behavior of sprayed deposits. 

FEA of the stresses in the UHMWPE cup is difficult, as the stresses exceed the elastic limit. Teoh et al. (2002) considered an 8 mm thick cup with a metal backing, a 32 mm diameter ball and a peak load of 2.2 kN (about 2.5 X body weight) for walking. Using the unrealistic condition that the compressive stress on the ball/UHMWPE interface could not exceed the uniaxial compressive yield stress (of 8 MPa), they predicted the compressive stress to be at this level over a surface region of diameter about 8 mm. However, a von Mises type yield criterion should be used. It requires a pressure of nearly three times the uniaxial yield stress to extrude the PE to the side of the joint (Section 8.2.4). 

A mechanical interaction of the abrasive grains with the workpiece usually leads to compressive residual stresses by localized elastic deformation and plastic flow. The predominance of mechanical process effects can be achieved by chip formation with increased ratio of micro-plowing. This usually occurs in grinding with small chip thickness and low cutting speeds (Fig. 2). 

Figure 7.12 Typical compressive cyclic stress-strain curves, (a) Fine-grained and coarse-grained Ti3SiC2. The dotted line is a linear elastic response expected forTi3SiC2 had kinking not occurred. Also included are the results on AI2O3 and Al for comparison [5] ...

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