Crack Path Simulation Research Articles

Crack observation methods, their application and simulation of curved fatigue crack growth

Abstract The observation of cracks with curved crack path has to be done optically. It is shown that a modified commercial flat bed scanner and a combination of a high-resolution scanner camera system with 10,000 × 10,000 pixels with a telecentric lens are appropriate for high-resolution (up to 8 μm/pixel) optical recording of multiple crack ends on sample areas up to 210 mm × 290 mm. The high-resolution photographs are suitable for determination of crack lengths. It is also possible to observe crack paths or geometrical crack tip parameters and strain fields by image correlation. The method is used to determine static crack resistance and cyclic crack growth curves on center crack tension and biaxial cruciform samples. Furthermore, the paper presents an improved finite element technique for the simulation of curved fatigue crack growth in a multiple arbitrarily pre-cracked isotropic sheet under biaxial plane stress loading applying a predictor–corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method including the consideration of the plastic limit loads. For this, the program PCCS-2D was extended to analyse the crack growth and the plastic limit load for each crack propagation step in a fully automatic simulation. The proposed solution algorithm provides a powerful tool for flaw assessment with the failure assessment diagram procedure in combination with a numerical crack path simulation. Finally, the simulation is verified experimentally.

Simulation of crack paths in functionally graded materials

Abstract One of the main interests of fracture mechanics in functionally graded materials is the influence of such an inhomogeneity on crack propagation processes. Using the Griffith’ energy principle, the change of energy has to be calculated, if the crack starts to propagate. In homogeneous linear-elastic structures (asymptotically precise) formulas for the energy release rate are known, but a direct transfer of these methods to functionally graded materials can lead to very inaccurate results. Moreover, the influence of the inhomogeneity on the crack path cannot be seen. Here, a simple model for functionally graded materials is introduced. For this model, a formula for the change of potential energy is derived, giving detailed information on the effect of the gradation on crack propagation.

Simulation of Curved Fatigue Crack Growth with Calculation of the Plastic Limit Load

In this paper a higher order crack path simulation algorithm for multiple interacting cracks is presented using piecewise parabolic curved increments including the consideration of the plastic limit loads. For this reason, the program PCCS-2D has been extended to analyse the crack growth and the plastic limit load for each crack propagation step in a fully automatic simulation. The proposed solution algorithm provides a powerful tool for flaw assessment with the FAD proce¬dure in combination with a numerical crack path simulation. Several numerical examples are pre¬sented to show the accuracy and the efficiency of the crack path simulation including the analysis of the plastic limit loads

チップ部品の鉛フリーはんだ接合部における疲労寿命のばらつき(<小特集>電子機器の熱・機械信頼性と機械工学)

This paper presents the assessment of thermal fatigue life scatter of solder joints for chip components. Crack path simulation was carried out by using the finite element method. Fatigue life was evaluated based on Manson-Coffin's law and Miner's rule. Analysis was designed by using an orthogonal table and the response surface methodology was used to demonstrate the sensitivity analysis. The case study to evaluate the worst and best values of fatigue lives shows the large difference in fatigue life. Asymmetrical solder joints have the larger dispersion of fatigue life because the chip component has two solder joints influencing on each other. It means that the interaction between both solder joints affects the dispersion of thermal fatigue life.

Threshold strength prediction for laminar ceramics from bifurcated crack path simulation

Abstract Thin compressive layers sandwiched between thicker tensile layers in laminar ceramics can stop unstable cracks. As shown by Lange and co-workers, the arrested crack propagates stably through the compressive layer under increasing load until a critical load or threshold strength is reached. In 4-point flexural loading tests, cracks can bifurcate after entering into the compressive layer. This paper presents finite element simulations of bifurcated crack paths and threshold strength prediction in two-dimensional approximation. In rather good agreement with experiments the calculated threshold strength increases with compression and is higher with bifurcated cracks than with straight cracks, and higher with loading axis parallel to the laminar plane than normal to it.

Simulation of simplified zigzag crack paths emerging during fatigue crack growth

When subjected to fatigue loading, microstructurally short cracks form zigzag shapes in single shear mechanisms due to nucleation, glide and annihilation of dislocations. Such crack progression is geometrically complicated and computationally expensive to model. This paper investigates the possibilities of efficiently modelling such growth behaviour by geometrical simplifications of the zigzag path. The crack path and the emerging plasticity was modelled by two different dislocation formulations and it was found that, irrespective of dislocation modelling technique, a valid geometrical approximation was to disregard the surface roughness except for the zigzag section closest to the crack tip.

4057 自動き裂進展解析によるはんだ接合部の破断寿命評価(G03-13 き裂進展(2),G03 材料力学)

In recent years, the development of the electronic device using the semiconductor is remarkable. In current advanced technology, it has succeeded in making the package which size is almost equal to the IC chip. Moreover for miniaturization and high integration of the electronic device, it has been fined in soldered joints divisions. However, the strength reliability becomes an important problem, since the thermal fatigue destruction is generated by thermal expansion difference between package and printed circuit board. In the case of chip, not only crack initiation but also crack propagation affects the number of cycles to failure of components. The former can be evaluated on the basis of Manson-Coffin's law. In this study crack path simulation was carried out by using an user subroutine and the number of cycles to failure with crack propagation was evaluated by using Miner's rule concept.

Crack path simulation and identification in polycrystalline alumina

A transgranular crack is observed in polycrystalline alumina (Lucalox). By a 2-D calculation, it is proposed that surface crack propagation is dominated by the grain cleavage plane rather than the high residual stresses from processing.

Crack Path Simulation by the MVCCI Method: Different Approaches and Applications

Crack Path Simulation by the MVCCI Method: Different Approaches and Applications

Numerical and Experimental Investigations of Curved Fatigue Crack Growth under Proportional Cyclic Loading

The present paper demonstrates that the common computer‐aided two‐dimensional crack path prediction can be considerably improved in accuracy by using a new predictor‐corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method. The numerical crack growth simulation is still based on a step‐by‐step technique, but uses a piecewise curved approximation of the crack path. By this method, both the new locus of the crack tip and the slope of the crack path at the crack tip can be computed simultaneously by the mode I and II stress intensity factors for only one virtual tangential crack extension with respect to the previous step. Furthermore, the paper presents a new finite element technique of calculating stress intensity factors of mixed mode problems by MVCCI Method. The procedure is devised to calculate the separated strain energy release rates by using the convergence of two separate calculations with different element sizes in the neighbourhood of the crack. The method provides robust calculation ability, even in the case of very coarse meshes. In order to evaluate the validity and efficiency of the proposed higher order crack path simulation method in relation to the well‐established basic strategies, experiments of curved fatigue crack growth are carried out with a specially designed specimen under proportional lateral force bending. In all investigated cases the computationally predicted crack trajectories show an excellent agreement with the different types of curved cracks that are obtained in the experiments as a function of the position of crack initiation.

Computational aspects of crack path development simulation in materials with nonlinear process zone

The issues addressed here are the accuracy and legitimacy of some strategies used in computational procedures simulating crack path development in materials exhibiting nonlinear behavior in the crack tip process zone. Relatively small errors in determination of the crack path deflection angle lead to a significant cumulative deviation of crack path over a finite crack length. The results presented here demonstrate that to ensure a consistent and accurate crack path simulation in material with a nonlinear process zone, the crack path probing segment must be continuously adjusted in coordination with the probing crack path deflection angle. Possible criteria of the crack path deflection in these materials are discussed here as well.

535 繊維-反応層-マトリックスの 3 層メソモデルにおけるき裂の直進と偏向の数値解析

535 繊維-反応層-マトリックスの 3 層メソモデルにおけるき裂の直進と偏向の数値解析