A particular case of interface cracks is considered. The materials at each side of the interface are assumed to have different yield strength and plastic strain hardening exponent, while elastic properties are identical. The problem is considered to be a relevant idealization of a crack at the fusion line in a weldment. A systematic investigation of the mismatch effect in this bi-material plane strain mode I dominating interface crack has been performed by finite strain finite element analyses. Results for loading causing small scale yielding at the crack tip are described. It is concluded that the near-tip stress field in the forward sector can be separated, at least approximately, into two parts. The first part is characterized by the homogeneous small scale yielding field controlled by J for one of the interface materials, the reference material. The second part which influences the absolute value of stresses at the crack tip and measures the deviation of the fields from the first part can be characterized by a mismatch constraint parameter M. Results have indicated that the second part is a very weak function of distance from the crack tip in the forward sector, and the angular distribution of the second part is only a function of the plastic hardening property of the reference material.

Articles you may be interested inLithiation-induced tensile stress and surface cracking in silicon thin film anode for rechargeable lithium battery Finite element modeling of indentation-induced superelastic effect using a three-dimensional constitutive model for shape memory materials with plasticity Elastic moduli, strength, and fracture initiation at sharp notches in etched single crystal silicon microstructures Constitutive modeling of silicon materials is currently restricted to the very early stage of deformation. Uniaxial tensile testing of monocrystals oriented for single glide is traditionally simulated by a scalar model relying on the so-called machine equation. The present work uses a crystal plasticity framework to identify the role of secondary slip systems in the yield region. A three-dimensional finite element model of a tensile apparatus is validated by comparison of its outputs to the results yielded by a scalar formulation. Best fits of the constitutive model of Alexander and Haasen to experimental data reveal strong variations in its parameters with temperature. An improved constitutive model for intrinsic silicon monocrystals deformed in single slip is described. Its parameters are identified as analytical functions of temperature. We show its excellent agreement with the observed steady state of deformation in stage I.

Following a convincing demonstration of the prediction power of the Gurson model for ductile fracture, it is now required to select realistic material parameters for practical applications of the model. In this paper, using studies on a smooth tensile specimen, a notched tensile specimen, a centre-cracked tensile panel and an analytical cell model, a sensitivity analysis of the material parameters is performed that includes the initial void volume fraction of the primary inclusions and the void volume fraction of the secondary inclusions when fitting the critical void volume fraction. Voids that nucleated from primary and secondary inclusions have been considered separately. It has been found that in either case the selection of material parameters for the finite element analyses is not unique, and the most significant parameter for the predictions is the nucleation burst strain. Some general conclusions concerning the selection of material parameters for the Gurson model have also been made.

A B S T R A C TThis study presents the effect of residual stresses on cleavage fracture toughness by using the cohesive zone model under mode I, plane stain conditions. Modified boundary layer simulations were performed with the remote boundary conditions governed by the elastic K-field and T-stress. The eigenstrain method was used to introduce residual stresses into the finite element model. A layer of cohesive elements was deployed ahead of the crack tip to simulate the fracture process zone. A bilinear traction-separation-law was used to characterize the behaviour of the cohesive elements. It was assumed that the initiation of the crack occurs when the opening stress drops to zero at the first integration point of the first cohesive element ahead of the crack tip. Results show that tensile residual stresses can decrease the cleavage fracture toughness significantly. The effect of the weld zone size on cleavage fracture toughness was also investigated, and it has been found that the initiation toughness is the linear function of the size of the geometrically similar weld. Results also show that the effect of the residual stress is stronger for negative T-stress while its effect is relatively smaller for positive T-stress. The influence of damage parameters and material hardening was also studied.

Structures subjected to severe cyclic loading may fail due to low cycle fatigue. During the latter part of the fatigue life the crack growth rate may increase due to crack growth from static failure modes. This was investigated numerically by Skallerud and Zhang (Int. J. Solids Struct. 34, 3141–3161, 1997) for a butt‐welded plate with a circular crack growing from the centre of the weld. The weld material was slightly overmatching, and for simplicity, base material properties were employed in the finite element model. The predicted crack growth rate was significantly underpredicted in the early part of crack growth. In the present investigation, more detailed material modelling was used, and some metallurgical aspects were addressed. The fatigue part of the crack growth was determined by using the computed cyclic J‐integral, and the static mode crack growth from ductile tearing is determined from computations accounting for void nucleation/growth/coalescence by means of a modified Gurson–Tvergaard model.

Solar silicon wafers are mainly produced through multiwire sawing. The sawing process induces micro cracks on the wafer surface, which are responsible for brittle fracture. Hence, it is important to scrutinize the crack geometries most commonly generated in silicon wafer sawing or handling process and link the surface crack to the fracture of wafers. The fracture of a large number of multicrystalline silicon wafers has been investigated by means of 4-point bending and twisting tests and a failure probability function is presented. By neglecting the material property variation and assuming that one surface crack is dominating the wafer breakage, 3D finite element models with various crack sizes (depth, length, and orientation) have been analyzed to identify the distribution of surface crack geometries by fitting the failure probability from the experiments. With respect to the 63% probability, the existing surface cracks in the wafers studied appear to have depth and length ratios less than 0.042 and 0.19, respectively. Furthermore, it has been shown that the surface cracks with depth in the range from 10 to 20 μm, length up to 10 mm and angles in the range of 30 deg–60 deg, can be considered as the most common crack geometries in wafers we tested. Finally, it has been found that the mechanical strength of the wafers tested parallel to the sawing direction is approximately 15 MPa smaller than those tested perpendicular to the sawing direction.

Solar wafer/cell breakage depends on the combination of the stresses generated in the handling and the presence of structural defects such as cracks. Suction process is a common loading during silicon wafer handling. This paper presents a systematic static and dynamic analysis of the suction process. Optimum suction pad diameter and locations are obtained by minimizing the stress distribution under both static and dynamic loading, and the effect of the impact time on the crack driving force is also investigated in this optimum situation. The results show that the four pads configuration with diameter of 20 mm placed in a rhombus shape with 18 and 38 mm diagonal lengths yields lowest maximum principle stress among the cases analyzed. In the dynamic fracture analyses, the maximum J integral appears at 800 and 1400 μs for continued holding and unloading cases after reaching the maximum load, respectively. The J integral for the unloading cases are always smaller than the holding cases. It has been found that when the impact time is longer than 3 s and 5600 μs the dynamic fracture mechanics analysis of the suction impact process can be replaced by a static fracture mechanics analysis for the holding and unloading cases, respectively.

Vibration is one of the most common loading modes during handling and transport of solar silicon wafers and has a great influence on the breakage rate. In order to control the breakage rate during handling and facilitate the optimization of the processing steps, it is important to understand the factors which influence the natural frequency of thin silicon wafers. In this study, we applied nonlinear finite element method to investigate the correlation of natural frequency of thin solar silicon wafer with material microstructures (grain size and grain orientation), thickness variation and crack geometry (position and size). It has been found that the natural frequency for anisotropic single crystal silicon wafer is a strong function of material orientation. Less than 10% thickness variation will have a negligible effect on natural frequency. It is also found out that cracks smaller than 20 mm have no dominant effect on the first five natural frequency modes anywhere in the silicon wafer.