scholarly journals SIMULATION OF CRACK PROPAGATION IN TWO DIMENSIONAL PROBLEMS

2010 ◽  
Vol 13 (4) ◽  
pp. 40-50
Author(s):  
Thien Tich Truong ◽  
Bang Kim Tran
Keyword(s):  
Crack Propagation ◽  
Strain Energy ◽  
Crack Path ◽  
Maximum Energy ◽  
Rate Theory ◽  
Stress Theory ◽  
Crack Trajectory ◽  
Minimum Strain Energy ◽  
Maximum Energy Release ◽  
Strain Energy Density Theory

Predicting crack trajectory when crack propagation occurs plays an important role in fracture mechanics problems because this will evaluate whether important areas of structure are heavily influenced by crack propagation. This article will introduce three theories to predict crack path, including maximum tangential stress theory, maximum energy release rate theory and minimum strain energy density theory. Besides, the FRANC2D program is used to simulate the crack propagation based on three above theories.

Fracture Under Combined Loads by Maximum-Energy-Release-Rate Criterion

1978 ◽  
Vol 45 (3) ◽  
pp. 553-558 ◽  
Author(s):  
C.-H. Wu
Keyword(s):  
Maximum Stress ◽  
Maximum Energy ◽  
Antiplane Shear ◽  
Combined Loads ◽  
Biaxial Load ◽  
Title Problem ◽  
Minimum Strain Energy ◽  
Energy Release Rate Criterion ◽  
Rate Criterion ◽  
Maximum Energy Release

The title problem is studied for the cases: (1) crack-perpendicular tension and crack-parallel shear, (2) plane biaxial load, (3) crack-parallel shear and antiplane shear, and (4) unidirectional load and antiplane shear. All the results are based on a fundamental investigation reported in references [1, 2], the results of which are partly exact, and partly asymptotic and numerical. Neither the maximum-stress nor the minimum-strain-energy-density criterion indicates a coupling between plane and antiplane loads.

Fracture of aluminum-epoxy layered composites containing cracks

1982 ◽  
Vol 17 (2) ◽  
pp. 75-78 ◽  
Author(s):  
E E Gdoutos
Keyword(s):  
Composite Plate ◽  
Strain Energy ◽  
Crack Extension ◽  
Critical Value ◽  
Layered Composites ◽  
Parallel Cracks ◽  
Two Parallel Cracks ◽  
Minimum Strain Energy ◽  
Uniaxial Compressive Stress ◽  
Strain Energy Density Theory

The plane problem of a composite plate consisting of two aluminum half-planes bonded together through an epoxy layer and containing two parallel cracks, one in the layer and the other in one of the half-planes was considered. The composite plate was loaded by a uniform uniaxial compressive stress distribution applied along the surfaces of the crack of either the layer or the half-plane. The critical value of the applied stress as well as the corresponding angle for crack extension were determined by using the minimum strain energy density theory. Valuable results governing the dependence of the critical failure stress of the composite plate as well as the angle of crack extension from the more vulnerable crack on the geometry of the plate were derived.

Quasi-Static Simulation of Crack Propagation on Elastic Material with Material Discontinuous Zone

2013 ◽  
Vol 746 ◽  
pp. 211-214
Author(s):  
Zhi Jia Sun ◽  
You Tang Li
Keyword(s):  
Crack Propagation ◽  
Deflection Angle ◽  
Crack Path ◽  
Circumferential Stress ◽  
Propagation Direction ◽  
Propagation Path ◽  
Stress Theory ◽  
Fem Method ◽  
The Matrix ◽  
Simulation Results

A numerical method to simulate the crack propagation based on the maximum circumferential stress theory is presented in this paper. The FEM method is used to estimate the influence of the material discontinuous zone on the propagation path of the crack placed in close to it in the matrix. When the crack grows, the FEM method uses the maximum circumferential stress theory to determine the propagation direction and the elements re-meshing program to ensure the accuracy of the crack-tip stress field. The crack propagation paths in the matrix with different material zone are simulated by the method. The simulation results show that the property of the material discontinuous zone influences the maximum deflection angle and its size influences the length of the deflected crack path.

Measurements of the velocity of crack propagation in glass plates

1963 ◽  
Vol 53 (1) ◽  
pp. 87-93
Author(s):  
John DeNoyer ◽  
Henry Pollack
Keyword(s):  
Crack Propagation ◽  
Energy Distribution ◽  
Strain Energy ◽  
Crack Velocity ◽  
Crack Path ◽  
Velocity Of Propagation ◽  
Glass Plates

Abstract The velocity of crack propagation in glass plates has been measured. The plates were strained until fractures were initiated. Measurements made over various small segments of the crack path show variations in crack velocity from 0.01 to about 4 km/sec. The velocity of propagation appears to be related to the strain-energy distribution. Regions of the plate where the strain energy was high prior to fracture yielded the highest crack velocities.

scholarly journals Crack Propagation in the Human Bone. Mode I of Fracture

2018 ◽  
Vol 26 (2) ◽  
pp. 59-70
Author(s):  
E. M. Craciun ◽  
A. Rabaea ◽  
M. F. Popa ◽  
C. I. Mihailov
Keyword(s):  
Crack Propagation ◽  
Strain Energy ◽  
Maximum Stress ◽  
Crack Path ◽  
Hilbert Problem ◽  
Mathematical Problem ◽  
Human Bone ◽  
Mode I ◽  
Crack Faces ◽  
Stress Criteria

Abstract The problem of crack propagation in human bone is studied. We for- mulate and solve the mathematical problem for the pre-stressed crack in Mode I of classical fracture. Using the boundary conditions on the crack faces in the bone, regarded as an elastic composite material, we solve our Riemann-Hilbert problem. Using generalized Sih's strain energy density generalized and maximum stress criteria we find the direction of the crack path in Iliac bone, regarded as a pre-stressed orthotropic composite.

scholarly journals A strain energy density theory for mixed mode crack propagation in rubber-like materials

2016 ◽  
pp. 1417 ◽  
Author(s):  
Abdelkader Boulenouar ◽  
Noureddine Benseddiq ◽  
Mohamed Merzoug ◽  
Nabil Benamara ◽  
Mohamed Mazari
Keyword(s):  
Energy Density ◽  
Crack Propagation ◽  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
Mixed Mode Crack ◽  
Strain Energy Density Theory

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

Crack Driving Force in Anisotropic Media due to Non-Elastic Deformation

2004 ◽  
Vol 261-263 ◽  
pp. 75-80
Author(s):  
G.H. Nie ◽  
H. Xu
Keyword(s):  
Elastic Deformation ◽  
Driving Force ◽  
Strain Energy ◽  
Elastic Stress ◽  
Complex Function ◽  
Crack Driving Force ◽  
Special Cases ◽  
Degree Of Anisotropy ◽  
Minimum Strain Energy ◽  
Orthotropic Media

In this paper elastic stress field in an elliptic inhomogeneity embedded in orthotropic media due to non-elastic deformation is determined by the complex function method and the principle of minimum strain energy. Two complex parameters are expressed in a general form, which covers all characterizations of the degree of anisotropy for any ideal orthotropic elastic body. The stress acting on the long side of ellipse can be considered as a crack driving force and applied in failure and fatigue analysis of composites. For some special cases, the resulting solutions will reduce to the known results.

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