Effects of Mixed-Mode and Crack Surface Convection in Rapid Crack Growth in Coupled Thermoelastic Solids

1999 ◽  
Vol 67 (1) ◽  
pp. 59-65 ◽  
Author(s):  
L. M. Brock

Two Green’s function problems for rapid two-dimensional steady-state crack growth governed by fully coupled (dynamic) linear thermoelasticity are analyzed. In Problem A, normal and in-plane shear line loads move on the insulated surfaces of a semi-infinite crack growing at a subcritical speed. Problem B involves only normal line loads, but crack surface convection is allowed. Problem A involves, therefore, mixed traction/displacement boundary conditions, while Problem B also exhibits mixed thermal boundary conditions. Robust asymptotic forms based on exact solutions for related problems reduce Problems A and B to coupled sets of integral equations. Both sets exhibit both Cauchy and Abel operators, but are solved exactly. The solutions show that Mode II loading couples the tangential crack face separation and discontinuity in crack-face temperature changes, while crack surface convection enhances thermal response, especially at large distances. [S0021-8936(00)03101-9]

2016 ◽  
Vol 8 (4) ◽  
pp. 573-587 ◽  
Author(s):  
R. R. Bhargava ◽  
Pooja Raj Verma

AbstractA problem of two equal, semi-permeable, collinear cracks, situated normal to the edges of an infinitely long piezoelectric strip is considered. Piezoelectric strip being prescribed out-of-plane shear stress and in-plane electric-displacement. The Fourier series and integral equation methods are adopted to obtain analytical solution of the problem. Closed-form analytic expressions are derived for various fracture parameters viz. crack-sliding displacement, crack opening potential drop, field intensity factors and energy release rate. An numerical case study is considered for poled PZT–5H, BaTiO3 and PZT–6B piezoelectric ceramics to study the effect of applied electro-mechanical loadings, crack-face boundary conditions as well as inter-crack distance on fracture parameters. The obtained results are presented graphically, discussed and concluded.


1972 ◽  
Vol 7 (2) ◽  
pp. 132-140 ◽  
Author(s):  
P B Lindley

The determination of tearing energy, i.e. the energy available for crack growth, is an essential prerequisite for the estimation of the fatigue life of rubber components. Three methods of determining tearing energy are considered: from changes in total energy, from crack surface displacements, and by comparison with known values for the same crack growth rates. It is shown by applying experimental and numerical techniques to plane-stress testpieces, not necessarily of uniform stress or thickness, that the methods are satisfactory.


2000 ◽  
Author(s):  
A. J. Rosakis ◽  
D. Coker ◽  
C. Yu ◽  
M. Ortiz

Abstract In this paper dynamic fracture behavior of unidirectional graphite-epoxy composite plates is investigated experimentally and numerically. Crack propagation experiments are conducted on thick unidirectional graphite-epoxy composite plates subjected to in-plane, symmetric and asymmetric, impact loading. The coherent gradient sensing technique (CGS) is used in conjunction with high-speed photography to visualize the crack growth events. Cracks are found to propagate at subsonic speeds in the Mode-I case, whereas in both mixed mode and Mode-II the crack tip speed clearly exceeds the shear wave speed of the laminate. In the case of symmetric loading (Mode-I), the crack tip speeds approach the Rayleigh wave speed of the composite (1500 m/s), however it never exceeds it as predicted by asymptotic analysis. The situation is found to be entirely different for growing shear (Mode-II) cracks. A shock wave emanating from the crack tip is observed in the optical patterns. This provides direct evidence that the crack propagates faster than the shear wave speed of the composite. The crack tip speed is then observed to jump to a level close to the axial longitudinal wave speed along the fibers (7500 m/s) and then to stabilize to a lower level of approximately 6500 m/s. This speed corresponds to the speed at which the energy release rate required for shear crack growth is non-zero as determined from asymptotic analysis. The CGS interferograms also reveal the existence of large-scale frictional contact of the crack faces behind the moving shear cracks. In addition high speed thermographic measurements are conducted that show concentrated hot spots behind the crack tip indicating crack face frictional contact. Finally, these experiments are modeled by a detailed dynamic finite element calculation involving cohesive elements, newly developed adaptive remeshing using subdivision and edge collapse, composites element, and penalty contact. The numerical calculations are calibrated on the basis of fundamental material properties measured in the laboratory. The numerical methodology is subsequently validated by direct comparison to optical experimental measurements (crack speed record and near tip deformation field structure). For shear crack growth the numerics also reveal the experimentally observed shock wave structure and confirm the optical observation of large-scale crack face contact.


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