A comparison of energy release rates, the J-integral and crack tip displacements

1977 ◽  
Vol 13 (2) ◽  
pp. 257-259 ◽  
Author(s):  
A. Luxmoore ◽  
M. F. Light ◽  
W. T. Evans
Keyword(s):  
Energy Release ◽  
Crack Tip ◽  
J Integral ◽  
Release Rates ◽  
Energy Release Rates

Research of Underfill Delamination in Flip Chip by the J-Integral Method

2004 ◽  
Vol 126 (1) ◽  
pp. 94-99 ◽  
Author(s):  
Bulu Xu ◽  
Xia Cai ◽  
Weidong Huang ◽  
Zhaonian Cheng
Keyword(s):  
Energy Release ◽  
Thermal Cycle ◽  
Flip Chip ◽  
Electronic Packages ◽  
J Integral ◽  
Release Rates ◽  
Energy Release Rates ◽  
Cycle Loading ◽  
Scanning Acoustic Microscope ◽  
Delamination Propagation

Fracture mechanics approaches have been used to study reliability problems in electronic packages, in particular, adhesion related failure in flip chip assembly. It was verified in this work that the J-integral with a special flat rectangular contour near the crack tip can be used as energy release rate at the interface between chip and underfill. Meanwhile, the delamination propagation rates at the interface was measured by using C-mode scanning acoustic microscope (C-SAM) inspection for two types of flip chip packages under thermal cycle loading. Finally, the half-empirical Paris equation, which can be used as a design base of delamination reliability in flip chip package, has been determined from the crack propagation rates measured and the energy release rates simulated.

On Energy-Release Rates for a Plane Crack

1981 ◽  
Vol 48 (3) ◽  
pp. 525-528 ◽  
Author(s):  
A. Golebiewska Herrmann ◽  
G. Herrmann
Keyword(s):  
Stress Field ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Static Stress ◽  
Plane Crack ◽  
J Integral ◽  
Release Rates ◽  
Energy Release Rates ◽  
Natural Description

Considered is a plane crack in a homogeneous, static stress field. The component of the Ji integral normal to the plane of the crack (J2) is shown not to be path-independent in the sense of the well-known J integral (≡ J1) parallel to the plane of the crack. The relation between the energy-release rate for rotation L and the integral J2 is established. It is finally suggested that the integrals L and M may provide a more natural description of energy-release rates (or forces) for plane cracks, rather than the integrals J1 and J2.

Concepts of Separated J-Integrals, Separated Energy Release Rates, and the Component Separation Method of the J-Integral for Interfacial Fracture Mechanics

2003 ◽  
Vol 70 (4) ◽  
pp. 505-516 ◽  
Author(s):  
T. Nishioka ◽  
S. Syano ◽  
T. Fujimoto
Keyword(s):  
Stress Intensity ◽  
Energy Release ◽  
Interfacial Crack ◽  
Component Separation ◽  
Separation Method ◽  
J Integral ◽  
Intensity Factors ◽  
Release Rates ◽  
Energy Release Rates ◽  
Component Separation Method

First, this paper presents the concepts of separated J-integrals and separated energy release rates. The path-independent separated J-integrals have the physical significance of energy flows into an interfacial crack tip from adjacent individual material sides or, equivalently, separated energy release rates. Thus, the J-integral and the energy release rate can be evaluated by the sum of the path-independent separated J-integrals. Second, the relations between the separated J-integrals and the stress intensity factors are derived. Third, the component separation method of the J-integral is extended for interfacial crack problems to allow accurate evaluation of the stress intensity factors. Finally, pertinent numerical analyses are carried out to demonstrate the usefulness of the separated J-integrals and the component separation method.

scholarly journals Energy release rate of the fiber/matrix interface crack in UD composites under transverse loading: debond-debond and debond-free boundary interactions

2019 ◽  
Author(s):  
Luca Di Stasio ◽  
Janis Varna ◽  
Zoubir Ayadi
Keyword(s):  
Energy Release ◽  
Finite Thickness ◽  
Fiber Content ◽  
J Integral ◽  
Transverse Loading ◽  
Release Rates ◽  
Closure Technique ◽  
Loading Direction ◽  
Energy Release Rates ◽  
Fiber Matrix

The effects of crack shielding, finite thickness of the composite and fiber content on fiber/matrix debond growth in thin unidirectional composites are investigated analyzing Representative Volume Elements (RVEs) of different ordered microstructures. Debond growth is characterized by estimation of the Energy Release Rates (ERRs) in Mode I and Mode II using the Virtual Crack Closure Technique (VCCT) and the J-integral. It is found that increasing fiber content, a larger distance between debonds in the loading direction and the presence of a free surface close to the debond have all a strong enhancing effect on the ERR. The presence of fully bonded fibers in the composite thickness direction has instead a constraining effect, and it is shown to be very localized. An explanation of these observations is proposed based on mechanical considerations.

Crack Propagation Analysis by Finite Differences

1973 ◽  
Vol 40 (4) ◽  
pp. 902-908 ◽  
Author(s):  
M. Shmuely ◽  
Z. S. Alterman
Keyword(s):  
Energy Release ◽  
Strain Energy ◽  
Crack Tip ◽  
Strain Energy Release ◽  
Numerical Schemes ◽  
Release Rates ◽  
Constant Length ◽  
Static State ◽  
Energy Release Rates ◽  
Strain Energy Release Rates

A finite-difference scheme for treating the dynamic stress field around a crack tip under plane-strain conditions, is proposed. The scheme is initially applied to the case of a crack of constant length which is suddenly opened in an infinite elastic medium loaded by a remotely uniform stress. By this, a numerical solution corresponding to the static state of stress is obtained which is compared with analytic solutions. It is shown that the numerically evaluated strain-energy-release rates are close to values calculated analytically. A modified scheme which presupposes a cuspated crack tip results in nearly the same strain-energy-release rates. Hence the validity of both numerical schemes is confirmed. For the numerical schemes adjusted to handle the propagating crack problem, the results represent a situation which is very close to reality; namely, the crack velocity accelerates up to a stage where propagation continues with a practically constant velocity. This terminal velocity moves from about 0.77 C2 to about 0.57C2 (C2 being the shear wave velocity). The last-mentioned velocity value corresponds to the cuspated crack model.

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