Peak stress

In 1971 a metal-backed polyethylene acetabular cup was introduced. This cup provided an eccentric socket which was replaceable, leaving the metal and replacing only the polyethylene. Because of the success of this component, metal-backed high density polyethylene (HDPE) liner is standard for prosthetic acetabular components. Research confirms that metal-backing reduces the peak stresses in the bone cement, and that HDPE forms a successfiil articulating surface for the prosthetic joint. 

FIG. 20-70 The influence of moisture as a percentage of sample saturation S on granule deformabihty. Here, deformation strain (AL/L) is measured as a function of applied stress, with the peak stress and strain denoted by tensile strength and critical strain (AL/L) of the material. Dicalcium phosphate with a 15 wt % binding solution of PVP/PVA Kolhdon VAG4. [Holm et al., Powder Tech., 43, 213 (1.9S.5J,] With land permission from Elsevier Science SA, Lausanne, Switzerland. 

Appleton and Waddington [40] present experimental evidence that pulse duration also affects residual strength in OFHC copper. Samples shock loaded to 5 GPa for 1.2 ps pulse duration exhibit poorly developed dislocation cell structure with easily resolvable individual dislocations. When the pulse duration is increased to 2.2 ps (still at 5 GPa peak stress) recovered samples show an increase in Vickers hardness [41] and postshock electron micrographs show a well-developed cell structure more like samples shock loaded to 10 GPa (1.2 ps). In the following paragraphs we give several additional examples of how pulse duration affects material hardness. 

In any structural application it is the peak stress which matters. At the peak, the fibres are just on the point of breaking and the matrix has yielded, so the stress is given by the yield strength of the matrix, d and the fracture strength of the fibres, (t, combined using a rule of mixtures... 

Consider the peak stress that can be carried by a chopped-fibre composite which has a matrix with a yield strength in shear of d (d = jd ). Figure 25.4 shows that the axial force transmitted to a fibre of diameter d over a little segment 8x of its length is... 

Fig. 25.3. The variafion of peak stress with volume fraction of fibres. A minimum volume fraction (VJ ) is needed to give any strengthening.

In this case the peak stress is equal to the maximum fibre stress. So at jc = 0... 

Fig. 5.7. The electrical charge observed at various peak stresses is shown for PVDF. The indicated behavior is nonlinear, but reproducible and independent of loading path.

The second special case is an orthotropic lamina loaded at angle a to the fiber direction. Such a situation is effectively an anisotropic lamina under load. Stress concentration factors for boron-epoxy were obtained by Greszczuk [6-11] in Figure 6-7. There, the circumferential stress around the edge of the circular hole is plotted versus angular position around the hole. The circumferential stress is normalized by a , the applied stress. The results for a = 0° are, of course, identical to those in Figure 6-6. As a approaches 90°, the peak stress concentration factor decreases and shifts location around the hole. However, as shown, the combined stress state at failure, upon application of a failure criterion, always occurs near 0 = 90°. Thus, the analysis of failure due to stress concentrations around holes in a lamina is quite involved. 

For [001] and [IlO] orientations where no stress is resolved onto <110] ordinary slip, <101] superlattice slip is observed up to the peak temperature. <101] dislocatiom predominantly lie along their screw orientation up to the peak temperature. This is consistent with the recent results of TEM observations on [001] si"gle crystals by Stucke et al. [9]. At temperatures below the peak, CRSS is much higher for the [001] orientation than for the [IlO] orientation. However, both the peak temperature and peak stress are lower for the former orientation than the latter. TTie lower peak temperature for the [001] orientation is associated with the occurrence of twiiming of the lll <112]-type above the peak temperature. Such twinning can not occur for the [IlO] orientation in compression. Deformation of [Il0]-oriented crystals above the peak is carried by slip on 111 <112]. 

The second shear modulus, Gj, is the peak stress 90° out of phase with the strain, divided by the peak strain. 

Output includes node displacements, member end forces and support reactions A three-dimensional model would produce more accurate results hut a two-dimensional analysis normally is sufficient for this type of structure. Members will be subjected to loads from both long and short walls. The member capacity used in the mode or the allowable deformation must be limited to account for the fact that the members will be subjected to simultaneous bi-axial loading. A typical capacity reduction factor is 25%. This factor reflects the fact that peak stresses from each direction rarely occur at the same time. 

Now as we have stated earlier we can represent the phase difference between the applied stress and strain as <5. So for a peak stress cr0 we can visualise a stress displaced by a phase difference S ... 

The stress varies over the sample (compact) surface such that the peak stress is (2 to 2.5)P at the center and Ou/3 at the periphery (where P is the average stress on the sample). Since PCr Ou for most explosives, and the criticality condition is P>PCr, effective hot spots cannot form near the sample periphery. Effective hot spots are also not generated at the center of the sample because inelastic deformation of the sample is a minimum near its center. As will be shown, A B claim that non-uniform inelastic deformation of the entire sample generates hot spots... 

The peak stress can be resolved into a component a0 cos S that is in place with the strain, related to the stored elastic energy and a component viscous loss of energy [1,3,9,10-13]. 

Sulphur concrete (without additives) will typically have a near-linear stress-strain curve up to failure, which occurs explosively at a strain usually between 0.0005 and 0.002. The peak stress varies from 20 to 70 MPa depending on the mix design. Sulphur concrete is thus a strong but brittle concrete material the brittleness need not necessarily be a grave disadvantage cast iron was used for a long period of time as a construction material. Any modification to the stress-strain behaviour should be evaluated carefully to see whether the modification is potentially useful. Two different approaches have been used to modify stress-strain behaviour. The modifications are (a) polymerization of the binder 04, j>, 17) and (b) use of the thermodynamically stable orthorhombic sulphur as the binder with alteration of the bond behaviour (3, 18). The matrices of both types of concrete are thus "modified" sulphur. 

In experiments with cultured cells it has been shown that osteocytes, but not periosteal fibroblasts, are extremely sensitive to fluid flow, resulting in increased prostaglandin as well as nitric oxide production [104, 105], Three different cell populations, namely osteocytes, osteoblasts, and periosteal fibroblasts, were subjected to two stress regimes, pulsatile fluid flow and intermittent hydrostatic compression [104], Intermittent hydrostatic compression was applied at 0.3 Hz with a 13-kPa peak pressure. The pulsatile fluid flow was a fluid flow with a mean shear stress of 0.5 Pa with cyclic variations of 0.02 Pa at 5 Hz. The maximal hydrostatic pressure rate was 130 kPa/sec and the maximal fluid shear stress rate was 12 Pa/sec. Under both stress regimes, osteocytes appeared more sensitive than osteoblasts, and osteoblasts more sensitive than periosteal fibroblasts. However, despite the large difference in peak stress and peak stress rate, pulsatile fluid flow was more effective than intermittent hydrostatic compression. Osteocytes, but not the other cell types, responded to 1 hour pulsatile fluid flow treatment with a sustained prostaglandin E2 upregula-... 

Second, we have learned from our investigation of the molecular origin of the stick-slip transition that adsorbed linear chains undergo a coil-stretch transition and produce a slip boundary condition above a critical stress gc [27-29]. The adsorbed chains at the die exit rim are expected to undergo a coil-stretch transition at nominal stresses Gstress distribution depicted by the thick curve in Fig. 15. 

Since fatigue always occurs at locations of stress concentrations or material imperfections, peak stresses and stresses at welding locations have to be calculated and evaluated. 

Although the Finite Element Method is still not very common for calculating the static strength of a vessel, it became a standard tool for computation of peak stresses (Figure 1) for fatigue analysis. 

Figure 1. Finite Element model of a clamp closure for calculation of peak stresses...

S H Threshold stress for fatigue Peak stress for traction law... 

Denoting the probability density function for fiber failure by [Pg.30]

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