Micro-yielding

Crazes thicken by drawing in new material, across the craze-bulk interface that stretches to a characteristic extension ratio. The plastic deformation occurs under plane strain conditions (Appendix C), in the plane containing the tensile stress direction and the craze advance direction. The bulk polymer, above and below the craze, remains elastic, but it does not constrain the craze opening, because the void creation means that the craze Poisson s ratio is zero. 

Crazes do not form unless the tensile strain exceeds a critical value, approximately 2% for polycarbonate and 0.4% for polystyrene, in air. We will see in Chapter 10 that these values are reduced when the polymer is exposed to certain liquids. If the applied strain barely exceeds the critical value, the crazes are widely spaced. The craze spacing decreases as the applied strain increases. This is further evidence that crazing is a yield process. 

Finger-like advance of cracks lying in a plane (a) Surface of polycarbonate fractured in a carbon tetrachloride environment the liquid has advanced down parallel channels, (b) Sketch of a proposed method of craze advance. 

The model for multiple crazing (Fig. 8.19b) has parallel crazes, regularly spaced with separation s. The problem is split into two parts, as before. In 

Stress analysis of craze growth in a tensile stress field, with stress-free areas shown as shaded (a) Single craze of length a and (b) array of equal length crazes, separated by s in the direction of the tensile stress. 

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Considering the model prerequisites for cohesive powders, this minimum normal (tensile) force limit Fn combines the opposite influences of a particle stiffness, micro-yield strength pf 3 Of or resistance against plastic deformation and particle distance distribution The last-mentioned is characterised by roughness height h, as well as molecular centre distance ap=o for -dU/da = F = 0 = F j ,force equilibrium. It corresponds to an abscissa intersection ai z of the constitutive consolidation function, Fig. 3. 

Polymer transition to brittle behavior is quickened to shorter times by increases in temperature, cyclic loading, stress resulting in micro-yields and stress concentrations. The effect of temperature is complex. Physical aging is a manifestation of small... 

The first step to improve understanding of the RCF behaviour of nitrided 32CrMoV13 steel is to measure its mechanical properties. Lamagn e et al. [5] have shown that micro yield shear stress (yield shear stress for a plastic deformation of 0.0002%) is a physical crito ia of endurance limit as for as RCF is concerned. However, its determination in the case of surfoce hardened material is mwe complex since it requires a local measuremoit by nano-indentation function of depth. Moreover the denting process... 

The study of nitrided 32CrMoV13 steel doit initiated RCF requires the knowledge of (i) the micro yield shear stress profile, required to define the endurance limit (ii) the hardening law of the material, necessary to describe the indentation process that involves plasticity (iii) residual stresses induce by the nitriding treatment. They contribute to stresses undergcme by the material during indentation and over-rolling. 

Micro yield shear stress and uniaxial hardening behaviour are usually measured by global compressive tests made on material samples. This process gives average values over the section of the sample. Therefore, to be relevant, this test must be made on uniform samples. Two uniform samples (A... 

The micro yield shear stress profile has flujs been obtained and is presented in figure 6. It decreases continuously fi om 1170 MPa at surface to 420 MPa at core. 

Figure 6. Nitrided 32CrMoV13 steel micro yield shear stress profile.

The RCF endurance limit, HI, is defined as the maximum contact pressure that can undergo a contact without overtaking the micro-yield stress of the material [5]. In the experiment conducted in this study, the endurance limit of nitrided 32CrMoV13 steel in the smooth case, that depends upon the contact equivalent radius, is equal to 2.65 GPa [11]. When a surface is dented, pressure peaks arise around the dent which generate local stress concentration. The maximum contact pressure that can support the dented contact without overtaking... 

This question points out the importance of the choice of the hardening treatment depending upon the aimed application. Hence it has been shown by Vincent et al. [1] (figure 1) that, for a nitrided steel, the rolling contact fatigue endurance limit of the material strongly depends upon the equivalent radius of contacting bodies because of the evolution of the maximum stress depth compared with a fixed micro-yield stress profile, linked to the material. 

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