Plane strain modulus 83

The adhesion energy is 2y, and the mutual plane strain modulus and radius of curvature are... 

A craze at the crack tip in glassy polymer has a crack opening displacement of 4 /rm. Given that the fracture toughness is 1 MNm / and the plane strain modulus is 1.5 GPa, calculate the length of the craze and the craze stress. 

Here, Eg is the plane strain modulus of the isotropic elastic substrate and the singular integral is defined in the sense of its Cauchy principal value (Muskhelishvili 1953). 

A laminated composite is made by bonding two thin strips of steel with a thin film of adhesive epoxy, as shown in Figure 4.11. To characterize the delamination resistance F of the epoxy-steel bond, a patch is intentionally left out in the center section to create a crack of total length 2a. The partially bonded plates are then pulled apart by opposed forces of magnitude P per unit width of the strips the load point deflection is denoted by 6. The plane strain modulus of the steel is E. Assume that the deformation of the strips is two-dimensional and that it can be described in the same way as the double cantilever configuration in Section 4.2.1. 

A plot of Ao versus D implied by (4.83) is shown in Figure 4.50, where it can be seen that the singularity is stronger than (weaker than) square root if the plane strain modulus of the film material is greater than (less than) the plane strain modulus of the substrate material. 

A surface with sinusoidal pertubartion of its nearly flat surface with wavelength that is less (greater) than Acr is stable (unstable) against spontane-sous growth of the perturbation amplitude. For a surface energy density of Us = I J/m, a plane strain modulus of A = 10 N/m and an applied stress of cjui = 10 N / m, this critical wavelength Acr is approximately 300 nm. 

For spheres of the same isotropic elastic material with plane strain modulus E and the same undeformed radius R, the deformed contact area is flat and its boundary is circular due to the symmetry of the configuration. According to the Hertz point of view, the normal stress distribution predicted for the contact area z = 0,0[Pg.645]

Figure 10 - Plane strain modulus as determinedfrom fracture test results from the (left) and S (rigftt) ESIS TC4 round robins.

For a rectangular rubber block, plane strain conditions were imposed in the width direction and the rubber was assumed to be an incompressible elastic solid obeying the simplest nonhnear constitutive relation (neo-Hookean). Hence, the elastic properties could be described by only one elastic constant, the shear modulus jx. The shear stress t 2 is then linearly related to the amount of shear y [1,2] ... 

ISO 14129 1997 Fibre-reinforced plastic composites - Determination of the in-plane shear stress/shear strain response, including the in-plane shear modulus and strength, by the plus or minus 45 degree tension test method... 

Therefore, the unidirectional translaminar (i.e. through-thickness) shear strength can be obtained for the maximum load and the in-plane shear modulus of elasticity, Gu, taken from the initial linear portion of the unidirectional shear stress-shear strain (ti2 - y 2) curve ... 

Thin plate wave modulus (plane strain or two-dimensional Young modulus)... 

Ideally, rubber toughening should be accomplished without substantial sacrifices in modulus. For each modified resin, flexural and Young moduli and plane-strain fracture toughness were determined. Examination of various fracture surfaces by scanning electron microscopy showed the effects of modifier composition on the morphology of these multi-phase materials as well as the prominent features of the fracture process. 

The explicit formulae given by Rosen55 are also of value. They are derived from a model consisting of a random assemblage of composite cylinders (Hashin and Rosen56 ) and expressed in terms of the axial Young modulus E, the Poisson ratio for uniaxial stress in the fibre direction v, the transverse plane strain bulk modulus k, the axial shear modulus G and the transverse shear modulus G. ... 

The first case considered is solute desorption during unconfined compression. We consider a two dimensional plane strain problem, see Fig. 1. A sinusoidal strain between 0 and 15 % is applied at 0.001 Hz, 0.01 Hz, 0.1 Hz and 1 Hz. To account for microscopic solute spreading due to fluid flow a dispersion parameter is introduced. Against the background of the release of newly synthesized matrix molecules the diffusion parameter is set to the value for chondroitin sulfate in dilute solution Dcs = 4 x 10 7 cm2 s-1 [4] The dispersion parameter Dd is varied in the range from 0 mm to 1 x 10 1 mm. The fluid volume fraction is set to v = 0.9, the bulk modulus k = 8.1 kPa, the shear modulus G = 8.9 kPa and the permeability K = lx 10-13m4 N-1 s-1 [14], The initial concentration is normalized to 1 and the evolution of the concentration is followed for a total time period of 4000 s. for the displacement and linear discontinuous. For displacement and fluid velocity a 9 noded quadrilateral is used, the pressure is taken linear discontinuous. 

S Fiber volume fraction in load- E Young s modulus for composite Plane strain Young s modulus... 

Here E is an effective Young s modulus of the polymer (E = E for plane stress and E/(l — f) for plane strain v = Poisson s ratio) and a is the half length of the craze. The craze displacement profile is computed from... 

Quasi-static Young s modulus measured by Hertzian indentation (b) Data taken from ref [5] (c) Measured by Dynamic Mechanical Thermal Analysis (D.M.T.A) at 1 Hz (T is taken as the temperature of the maximum in tan 5) (d) (7y and Oy are the yield stress under uniaxial and plane strain compression, respectively, for an equivalent strain rate of 5x10" s" (see ref... 

C is the so-called plane-strain viscoelastic creep compliance. It is connected to the relaxation modulus E(t) and Poisson s ratio v(t) by... 

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