Shear stress-strain curve

The curves for 3M XP251S fiberglass-epoxy are shown in Figures C-1 through C-5 [C-1]. Curves are given for both tensile and compressive behavior of the direct stresses. Note that the behavior in the fiber direction is essentially linear in both tension and compression. Transverse to the fiber direction, the behavior is nearly linear in tension, but very nonlinear in compression. The shear stress-strain curve is highly nonlinear. The Poisson s ratios (not shown) are essentially constant with values v.,2 =. 25 and V21 =. 09. 

Figure C-5 Shear Stress-Strain Curve for 3M XP251S Fiberglass-Epoxy (Adapted from [C-1])...

FIG. 13.72 Shear stress-strain curves for PMMA at 22 °C under different pressures at a strain rate of approximately 4 x 10-4 s. The filled circles connect all fracture points in a fracture envelope. 

The shear behavior also involves matrix cracking and fiber failure.26 However, the ranking of the shear stress-strain curves between materials (Fig. 1.6) differs appreciably from that found for tension (Fig. 1.5). Preliminary... 

Fig. 1.6 Shear stress-strain curves measured for 2-D CMCs.

Fig.l. 37 Normalized in-plane shear stress-strain curves with the non-dimensional parameter W indicated. 

Triaxial extension Direct shear Stress-strain curve (same as triaxial compression)... 

Consolidated undrained Shear stress-strain curve Consolidation curve Drained strength parameters (Cd,d) Consolidation time ((50, f,oo)... 

Fig. 4.4. Design of bonded lap joint (Ref. 19). (a) Idealised adhesive shear stress/strain curve. (f>) Design of bonded double-lap joints.

This high load-bearing capacity in compression is also exhibited in shear. Figure 13.5 shows the shear stress-strain curves for a series of urethane elastomers. It is important to emphasize that polyurethanes are elastomers even at very high hardness values whereas conventional elastomers have lost a considerable amount of elastic properties at the hardness regions of greater than 75 IRHD. 

Fig. 4.21 (Color) Relaxed shear stress-strain curves of 22 materials, rescaled such that all have unit slope initially and reach maximum at 1. The renormalized Frenkel model Eq. (4.8) is shown (in heavy black line) for comparison [6]. With kind permission of Dr. Yip...

Figure 1. Shear stress-strain curves for epoxy-nitrile adhesive bonds after 8 weeks exposure to different environments. From ref. 13 by courtesy of Applied Science Publishers Ltd.

Figure 11.17 Shear stress-strain curves for PMMA showing fracture envelope. (Reproduced with permission of Rabinowitz, Ward and Parry, J. Mater. Set, 5, 29 (1970))...

The foregoing analysis of the skin-doubler specimen shows that it is essential to know the stiffness characteristics of the adhesive. Since good design practice places bond lines in shear, it was decided that the shear modulus is the primary stiffness parameter. Furthermore, it is recognized that more than the initial portion of the shear stress-strain curve was required. It was clear that the total curve was not linear. It was anticipated that the nonlinearity portion would bear heavily on creep and fatigue performance. Accordingly, the primary requirements for the strain measuring device were set as follows ... 

FIGURE 4. Shear stress-strain curve produced by the KGR-1 extensometer. 

Herein, L is the length of the cylinder, T is the appUed torque, r is the radial distance, J is the polar second moment of area and G is the shear modulus. These equations are developed assuming a linear relation between shear stress and strain as well as homogeneity and isotropy. With these assumptions, the shear stress and strain vary linearly with the radius and a pure shear stress state exists on any circumferential plane as shown on the surface at point A in Fig. 2,2. The shear modulus, G, is the slope of the shear stress-strain curve and may be found from. 

Other less well-known types of nonlinearities include interaction and intermode . In the former, stress-strain response for a fundamental load component (e.g. shear) in a multi-axial stress state is not equivalent to the stress-strain response in simple one component load test (e.g. simple shear). For example. Fig. 10.3 shows that the stress-strain curve under pure shear loading of a composite specimen varies considerably from the shear stress-strain curve obtained from an off-axis specimen. In this type of test, a unidirectional laminate is tested in uniaxial tension where the fiber axis runs 15° to the tensile loading axis. A 90° strain gage rosette is applied to the specimen oriented to the fiber direction and normal to the fiber direction and thus obtain the strain components in the fiber coordinate system. Using simple coordinate transformations, the shear response of the unidirectional composite can be found (Daniel, 1993, Hyer, 1998). At small strains in the linear range, the shear response from the two tests coincide. 

Actual adhesive shear stress-strain curves like those in Fig. 13 are simplified for analysis purposes. The most widely used model is the linearly elastic, perfectly plastic model developed by the author originally under contract to NASA Langley in the early 1970s. This model is described in Fig. 15 and is the basis of the A4E. series of computer codes, of which the A4EI code for stepped-lap joints and doublers covering variable adhesive properties and adhesive porosity and voids is perhaps the best known. This particular code was developed under contract to the USAF at the Wright Laboratories in Dayton (see [14]). 

Fig. 32. Adhesive shear stress-strain curves and mathematical models (after...

Tubular specimens (thin walls) can also be used and do not require a Nadai correction (Nadai 1931). The specimen geometry used by Gali et al. (1981) is presented in O Fig. 19.12b. Again, relevant properties are determined from the shear stress-strain curve. 

The most recent literature shows that all the test methods described above do not show a systematic variability in the shear stress-strain curves (Althof and Neumann 1974 Jeandreau 1993 ... 

There is a wide variety of shear tests. All the test methods described in this chapter do not show a systematic difference in the shear stress-strain curves. Torsion tests are the most accurate. However, torsion devices are not common in most laboratories. In case a torsion machine is not available, the TAST is probably the simplest and most reliable technique to use. 

Because the Mooney rheometer is a rotational instrument, the deformation is shear. The torque is proportional to shear stress. Since the rotational speed is constant, the time is proportional to shear strain. Therefore, it is a shear stress-strain curve, which is analogous to the more familiar tensile stress-strain curve. 

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