Plain strain condition

The equations above are valid for plane-stress situations, i.e. for thin sheets. For thicker sheets plain-strain conditions occur at the crack tip. In that case for a thick plate of infinite width containing a crack of length 2a the fracture stress is... 

The thickness of the TDCB specimens (S = 10 mm) is sufficient to ensure plain strain conditions. It should be noted that during the test the arms remain within their elastic limit. Therefore, from simple beam theory [7], and by the use of linear elastic fracture mechanics, the strain energy release rate of the adhesive can be obtained using Eqn. 2, where P is the load at failure and E, is the substrate modulus. The calculated adhesive fracture energy was employed in the simulation of the TDCB and impact wedge-peel (IWP) tests. 

Kic is the critical stress intensity factor for static loading and plain-strain conditions of maximum constraint represents a minimum value for thick plates. 

When the size of the plastic zone becomes nearly equal to the thickness of the specimen, plain strain conditions do not exist any more. In the plain strain condition, the plane of fracture instability is normal to the axis of the principal tensile stress. There is zero strain in the direction normal to both the axis of applied tensile stress and the direction of crack growth. The crack propagates in a direction perpendicular to the tensile stress (Stage 2). A shear decohesion also contributes to crack propagation [104]. 

This normal stress must operate in order to maintain plain strain conditions. Problem 2.8.1 Show that... 

Equation (6.42) indicates, for example, that with a root radius of 0.5 mm the corresponding TF is 1.83. Entering the curve of Fig. 6.25 with this value it yields a ductility loss of about 90 %. A rather big warning mark must be introduced at this time since this actually means that a material that imder uniaxial traction fails at a deformation of 35 % under plain strain condition will not reach more than 3.5 % strain. 

Fig. 6.24 Notch root strain reduction consequent the passage from a plain stress (uniaxial) to a plain strain condition (multiaxial)...

Hertz stress and the consequent increase in maximum stress of around 34% is clearly visible It may be noted that, in calculating the von Mises stress, plain strain conditions have been assumed and the transverse stress, assessed using a value of Poisson s ratio of 0.28, has been included in the calculation. 

Equations 1 and 2 can be used to predict SCXj failure in any PE product if Y can be determined and SCG occurs under plain strain conditions. The limitations are (1) the obal stress should be less than about half the yield point at the test temperature to avoid a significant amount of macroscopic creep in the specimen, (2) the test temperature should be... 

To simulate an axial crack driven by hoop stress, we consider CL growth in plain strain conditions under constant load cr. The process b ins under conditions ... 

---