Maximum shear strain

Xg (Xg ) = maximum tensile (compressive) normal strain in the 1-direction Yg (Yg ) = maximum tensile (compressive) normal strain in the 2-direction Sg = maximum shear strain in the 1-2 coordinates... 

As With the shear strength, the maximum shear strain is unaffected by the sign of the shear stress. The strains in principal material coordinates, 1- yi2 be found from the strains in body coordinates by transformation before the criterion can be applied. 

Shear stress-strain data can be generated by twisting (applying torque) a material specimen at a specified rate while measuring the angle of twist between the ends of the specimen and the torque load exerted by the specimen on the testing machine. Maximum shear stress at the surface of the specimen can be computed from the measured torque that is the maximum shear strain from the measured angle of twist. 

Manning (1947) has shown that the maximum shear strain energy theory of failure (due to Mises (1913)) gives a closer fit to experimentally determined failure pressures for monobloc cylinders than the maximum shear stress theory. This criterion of failure gives ... 

At the instant of contact between a sphere and a flat specimen there is no strain in the specimen, but the sphere then becomes flattened by the surface tractions which creates forces of reaction which produce strain in the specimen as well as the sphere. The strain consists of both hydrostatic compression and shear. The maximum shear strain is at a point along the axis of contact, lying a distance equal to about half of the radius of the area of contact (both solids having the same elastic properties with Poisson s ratio = 1/3). When this maximum shear strain reaches a critical value, plastic flow begins, or twinning occurs, or a phase transformation begins. Note that the critical value may be very small (e.g., in pure simple metals it is zero) or it may be quite large (e.g., in diamond). 

By neglecting the chain extension it is assumed that Wb=Wbs. Thus the observation that Wb is approximately constant for fibres of the same polymer with different degrees of orientation means that not only a constant critical shear stress, rb, but also a maximum shear strain, (0-0b), is a useful criterion of... 

The concept of a maximum shear strain is supported by the experimental relationship for the lifetime of a polymer fibre. For many polymer fibres the observed lifetime or the time to failure fb is given by... 

As shown in Fig. 10, the shear strain is proportional to the relative displacement of two parallel aligned adjacent chains. Therefore, it seems plausible to assume that the maximum shear strain value /3=( -8b) at which fracture of the fibre is initiated will be related to a critical overlap length between adjacent... 

The functions t(x) and (x) are depicted in Fig. 20. The maximum shear stress rm, which occurs for x=pl4 or at a (maximum) shear strain ofp/(4dc) is defined as the ultimate shear strength r0... 

Fig. 60 The angles of the domain axis in the unloaded state, 0 after loading at t-0, 0O at the time of fracture and the maximum shear strain p... 

The maximum shear strain in engineering units is fb=2/J, which corresponds to the value p(4dc) l in the Frenkel model discussed in Sect. 2.5.1. The relative displacement, xy of adjacent chains shown in Fig. 57 is limited by the maximum value 2/3 for larger displacements the attracting force decreases rapidly and failure is initiated. It is further assumed that A0(tb) [Pg.85]

The maximum shear strain criterion is now applied for the calculation of the creep curve up to fracture for increasing creep stress. The total creep strain of the fibre, q(f), is the sum of the elastic strain, cf, and the viscoelastic plus plastic strain, cj(f),... 

The proposed model for creep rupture based on the condition of maximum shear strain and the Eyring reduced time model explain the observed relations concerning the lifetime of aramid, polyamide 66 and polyacrylonitrile fibres. However, with increasing temperatures, in particular above 300 °C, chemical degradation of PpPTA also determines the lifetime. Furthermore, the model... 

The test piece assembly is strained in a tensile machine at 5 1 mm/min until a maximum shear strain of 30 % is reached. Mechanical conditioning is optional but, if used, five conditioning cycles are applied before the measuring cycle. No details of apparatus to measure the strain are given but this could be a dial gauge or, with a stiff tensile machine, the crosshead movement. 

Schall et al. indented colloidal crystals using a needle with an almost hemispherical tip of diameter 40 dm, inducing a strain field in which tine maximum shear strain lies well below the contact surface. The tip diameter, particle radius and crystal thickness in their experiments were chosen to be similar to parameters in typical metallic nano-indentation experiments. The authors discussed their observations using a model that addresses the role played by thermal fluctuations in the nucleation and growth of dislocations. 

Static load which causes creep of adhesive joints requires time-dependent knock-down factors. With a requirement of maximum shear strain of 0.1 after 10 years, some flexible adhesives already require extremely low factors (0.001-... 

A test method for shear modulus is described in ISO 1827 (BS90.3, Part A14). A bonded quadruple shear test piece, which may or may not have prcvk u.sly been mechanically conditioned, is deformed to a maximum shear strain of. 30%, and the result is reported as shear modulus at 25% strain. A second method in the same standard involves loading the test piece so that adhesion strength between rubber and substrate can be determined. No corresponding ASTM method is available. 

To verify this postulate, two CPNC specimens were prepared, one sheared dynamically between parallel plates (disks) at >= 100 rad/s and y = 40% for 15 min, and another just inserted into the rheometer, melted, but not sheared. To determine the clay orientation, the specimens were microtomed close to the disk border (maximum shear strain) in the planar and perpendicular directions and then observed under the high-resolution transmission electron microscope [Perrin, 2002]. In the first specimen the well-dispersed clay platelets (see Figure 16.8) were found to be oriented perpendicular to the stress direction, while in the second, unsheared specimen, the exfoliated, often bent platelets were randomly oriented. 

In 1996, Pal studied the effect of droplet size and found it had a dramatic influence on emulsion rheology (62). Fine emulsions have much higher viscosity and storage moduli than the corresponding coarse emulsions. The shear thinning effect is much stronger in the case of fine emulsions. Water-in-oil emulsions age much more rapidly than oil-in-water emulsions. More recently, Lee et al. (63) and Aomari et al. (64) examined model emulsions and found that a maximum shear strain existed which occurred around 100s. ... 

Soydemir, 1994,Tatsuokaetal., 1984,Tokimatsu Seed 1984,1987). The volumetric strain is also affected by the maximum shear strain amplitude induced by cyclic loading. It increases with cyclic strain amplitude and reaches an asymptotic value at a strain level of 10 to 15%. The maximum shear strain reached for each specimen m the current study is 12%. Figure 1 Ic shows a comparison of the results for clean sand from the current study with the data from the literature shown in F igures lla-b. The current data for clean sands fall in the range reported in the literature for the appropriate shear strain amplitude levels. 

Controlled strain (or, more properly, controlled displacement) oscillatory shear instruments, exemphfied by the Weissenberg Rheogoniometer [Macsporran and Spiers, 1982] readily facilitate tests in which independent measurements of both changing length scales and time scales of applied deformation can be performed. In this way it is, in principle, possible to separate effects due to strain and strain rates as the frequency of oscillation may be held constant while the maximiun (cyclic) shear strain amplitude is varied. Alternatively, the frequency of deformation can be varied at constant maximum shear strain amplitude. 

Kinloch(4) observed that the selection of appropriate failure criteria for the prediction of joint strength by conventional analysis is fraught with difficulty. The problem is in understanding the mechanisms of failure of bonded joints, and in assigning the relevant adhesive mechanical properties. Current practice is to use the maximum shear-strain or maximum shear-strain energy as the appropriate failure criterion. However, the failure of practical joints occurs by modes including, or other than, shear failure of the adhesive. This difficulty has led to the application of fracture mechanics to joint failure. 

Fig. 3. A schematic diagram showing the distribution of principal (cpmax) 3nd maximum shear strains (ymax) at four locations on the vertebral body under compression, anterior-posterior shear, and lateral shear loads (Frei 1997). The data show that the end plate is subjected to a greater percentage deformation in compression loading than under either anterior-posterior or lateral shear loading. Also, the vertebral rim, and presumably the annulus, is subjected to larger deformations under both anterior-posterior shear and lateral shear loading, while the end plate incurs much less deformation in shear loading...

The authors [6] suggest the term shearability , Sm, for the maximum shear strain that a homogeneous crystal can withstand. It is defined by Sm = argmax o-(s), where a(s), is the resolved shear stress and s is the engineering shear strain in a specified slip system. The relaxed shear stress, (7 in Table 4.2 is normalized by Gr. In this table, experimental and calculated values of the relaxed shear vales of Gr are given. For details on these calculations, refer to the work of Ogata et al. [6]. 

Using the WLF (49) equation to model the effect of temperature on the material viscosity Robertson went on derive an equation for the maximum shear strain... 

It is important to note that 3D nonlinear elastic-plastic finite element simulations were performed, while stiffness reduction curves were used for calibration of the material model and for determining (minimal) finite element size. It should also be noted that the largest FEM model had over 0.5 million elements and over 1.6 million DOFs. However, most of simulations were performed with smaller model (with 150 K elements) as it represented mechanics of the problem with appropriate level of accuracy. Working FEM model mesh is shown in Figure 2. The model used, features 484,104 DOFs, 151,264 soil and beam-column elements, and is intended to model appropriately seismic waves of up to 10 Hz, for minimal stiffness degradation of. GjGmax = 0.08, maximum shear strain of y = 1% and with the maximal element size... 

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