Comparison of Various Criteria Determining the Direction of Crack Propagation Using the UDMGINI User Procedure Implemented in Abaqus

This paper describes a method of predicting the direction of crack propagation implemented by user subroutines in the Simulia-Abaqus FEA system with the use of the extended finite element method (X-FEM). This method is based on displacements and stresses according to Westergaard’s solution of Griffith’s crack problem. During the calculations, in each crack increment, the algorithm reads the stresses and displacements in the model around the crack tip, calculates the criterion values at the read points, reduces them to a unit distance from the crack tip, fits a polynomial to these points, and finds the minimum of the function closest to the last propagation angle. The algorithm also decides when the crack grows, depending on a chosen criterion. Four criteria have been implemented to predict the direction of failure propagation: the maximum principal stress criterion, the Ottosen–Podgórski criterion, the new criterion described here based on the minimum component values of the displacement vector, and the maximum circumferential tensile stress (MTS). These criteria were verified in two tests: the three-point bending test of the notched beam and the anchor pull-out test. For these tests, the criterion built into Simulia Abaqus does not correctly define the crack path, which causes the crack propagation direction to “rotate” when simulating the fracture. The criteria developed here, in most cases, determine the crack path and the maximum force very well compared to real laboratory tests.

Analysis of the bi-material interface cracks based on configurational forces

In this paper, an innovative interface fracture criterion is proposed based on the concept of configurational forces in material space. In this criterion, the crack tip configurational forces as driving force is introduced to describe the interface crack evolution under mixed mode loading conditions. And it assumes that the interface crack propagates due to the competition of resultant of configurational forces with interface fracture toughness. The analytical expression of the configurational forces are obtained by differentiating the elastic strain energy density and conservative integral for interface cracks. And the relation of interface crack tip configurational forces with classical complex intensity factors are obtained through strict mathematical deduction. The interface crack tip configurational forces are evaluated for a classic interface crack problem covering a wide range of bi-material oscillation index. The configurational forces based interface fracture criterion is validated through series interface fracture experiments. The proposed criterion may provide a novel framework for analysis of interface fracture under complex loading conditions.

Dynamic performance for piezoelectric bi-materials with an interfacial crack near an eccentric elliptical hole under anti-plane shearing

The purpose of this paper is to evaluate the stress concentration at the tip of a permeable interfacial crack near an eccentric elliptical hole in piezoelectric bi-materials under anti-plane shearing. Fracture analysis is performed by Green’s function method and the conformal mapping method, which are used to solve the boundary conditions problem. The mechanical model of the interfacial crack is constructed by interface-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack-tips can be derived. The validity of the present method is verified by comparing with a crack emerging from the edge of a circular hole as a reference. Numerical cases reveal parametric dependence of DSIFs on the geometry of eccentric elliptical holes and interfacial cracks, the characteristics of the incident wave, the equivalent piezoelectric elastic modulus and piezoelectric parameters. The results illustrate that the eccentric distance has a great effect on the stress concentration at the crack tip, which may be harmful to the normal service of piezoelectric devices and materials. In addition, the method proposed in this paper can also deal with non-eccentric problems and has wider applicability.

Fracture and Fatigue Analyses of Cracked Structures Using the Iterative Method

It is a quite challenging subject to efficiently perform fracture and fatigue analyses for complex structures with cracks in engineering. To precisely and efficiently study crack problems in practical engineering, an iterative method is developed in this study. The overall structure which contains no crack is analyzed by the traditional finite element method (FEM), and the crack itself is analyzed using analytical solution or other numerical solutions which are effective and efficient for solving crack problems. An iteration is carried out between the two abovementioned solutions, and the original crack problem could be solved based on the superposition principle. Several typical crack problems are studied using the present method, showing very high precision and efficiency of this method when making fracture and fatigue analyses of structures.

Study on the Fracture Process Zone near the Mode I Dynamic Crack Tip

Evaluation of the shape and size of the fracture process zone near the mode I dynamic crack tip is still a problem unsolved completely at present. The research on the relationship between the fracture process zone and crack velocity near the mode I dynamic crack tip is quite limited, and some researchers have also developed experimental methods or numerical methods. In this research, based on the theory of elastodynamics and the complex stress function method, an approximate method for solving the mode I dynamic crack problem was proposed. The fracture process zone near the mode I dynamic crack tip was analyzed. The results showed that the areas of the fracture process zone determined based on the approximate method are nearly the same as the results obtained based on the well-known stress fields. The approximate method could provide a good reference for determining the fracture process zone near the mode I dynamic crack tip since no analytic methods had been found for evaluating the fracture process zone near the dynamic crack tip to the authors’ knowledge.

Predicting Silicon Die Breaking Force in Semiconductor Package Assembly through Mechanical Simulation

Die crack is a common problem in the semiconductor industry and being able to predict the breaking force at a given loading condition could help prevent such crack problem. This paper presents the use of mechanical simulation in predicting the force at which the silicon die breaks in semiconductor package assembly process. A computer simulation with finite element analysis (FEA) technique was used. The applied force or displacement in a die bending simulation with 3 mm, 4 mm and 15 mm support span was varied until the resulting maximum principal stress of the die becomes equal to its fracture strength. Results revealed that the breaking force for the 70 µm die with 6 mm width is around 5 N for the 3 mm support span and only around 1 N for the 15 mm support span. With the good agreement between modeling and actual results, the study showed that mechanical simulation is an effective approach in predicting die breaking force and can be used to simulate different mechanical loads in the package assembly where possible die crack could happen and be avoided. This is a fast and cost-effective way of assessing risk of die crack and obtaining package assembly process parameters and specifications that are safe to the silicon die.

Investigation on Die Crack in a Stacked Die Package Using Finite Element Analysis

Die crack is one of the problems in stacked die semiconductor packages. As silicon dies become thinner in such packages due to miniaturization requirement, the tendency to have die crack increases. This study presents the investigation done on a die crack issue in a stacked die package using finite element analysis (FEA). The die stress induced during the package assembly processes from die attach to package strip reflow was analyzed and compared with the actual die crack failure in terms of the location of maximum die stress at unit level as well as strip level. Stresses in the die due to coefficient of thermal expansion (CTE) mismatch of the package component materials and mechanical bending of the package in strip format were taken into consideration. Comparison of the die stress with actual die crack pointed to strip bending as the cause of the problem and not CTE mismatch. It was found that the die crack was not due to the thermal processes involved during package assembly. This study showed that analyzing die stress using FEA could help identify the root cause of a die crack problem during the stacked die package assembly and manufacturing as crack occurs at locations of maximum stress. The die crack mechanism can also be understood through FEA simulation and such understanding is very important in coming up with robust solution.