G.P. Potirniche

Analysis of crack tip plasticity for microstructurally small cracks using crystal plasticity theory

Crack tip plastic zone sizes and crack tip opening displacements (CTOD) for stationary microstructurally small cracks are calculated using the finite element method. To simulate the plastic deformation occurring at the crack tip, a two-dimensional small strain constitutive relationship from single crystal plasticity theory is implemented in the finite element code ANSYS as a user-defined plasticity subroutine. Small cracks are modeled in both single grains and multiple grains, and different crystallographic conditions are considered. The computed plastic zone sizes and CTOD are compared with those found using conventional isotropic plasticity theory, and significant differences are observed.

Atomistic modelling of fatigue crack growth and dislocation structuring in FCC crystals

Fatigue damage in face-centred cubic crystals by dislocation substructuring and crack growth was computationally simulated at the atomic scale. Single-crystal copper specimens with approximately 200 000 atoms and an initial crack were subjected to fatigue loading with a constant strain amplitude of εmax=0.01 and a load ratio of R=εmin/εmax=0.75. Cyclic plastic deformation around the crack tip is the main influencing factor for the propagation mechanisms of nanocracks. The main crack-propagation mechanisms occurred either by void nucleation in the high-density region near the crack tip or by fatigue cleavage of the atomic bonds in the crack plane. Fatigue crack growth at grain boundaries was also studied. For high misorientation angle grain boundaries, the crack path deviated while moving from one grain to another. For low crystal misorientations, the crack did not experience any significant out-of-plane deviation. For a large crystal misorientation, voids were observed to nucleate at grain boundaries in front of the crack tip and link back with the main crack. During fatigue loading, dislocation substructures were observed to develop throughout the atomic lattices. Fatigue crack growth rates for nanocracks were computed and compared with growth rates published in the literature for microstructurally small cracks (micron range) and long cracks (millimetre range). The computed growth rates for nanocracks were comparable with those for small cracks at the same stress intensity ranges and they propagated below the threshold for long cracks.

Finite element modeling of microstructurally small cracks using single crystal plasticity

Abstract Finite element simulations of small fatigue cracks were performed using crystal plasticity theory to describe the deformation behavior near the crack tip. A rate-independent small strain formulation from crystal plasticity theory was implemented. Constant amplitude loads were applied, with a load ratio of R =0.3. Crack opening stresses and crack tip opening displacement ranges were simulated as the crack grew in a single grain, as well as when the crack grew toward a grain boundary. Crack growth in single grains indicated that stabilization of the crack opening stresses occurs relatively rapidly (5–10 μm of crack growth). Studies of crack growth toward a grain boundary revealed that, depending on the orientation of the adjacent grain, the crack growth rate is significantly affected. If the angle of misorientation between the two adjacent grains is small, the neighboring grain can increase the growth rate near the grain boundary. If the misorientation angle is high, the fatigue crack growth rate will be significantly slowed near the grain boundary.

On the growth of nanoscale fatigue cracks

We identify nanoscale mechanisms of fatigue-crack growth in copper single crystals using molecular dynamics. By quantifying the nanoscale fatigue-crack growth rates, we can compare the growth rates for fatigue cracks on microstructural and macrostructural length scales. Computed crack growth rates in the nanometer range are shown to be very similar to those experimentally measured for small cracks (micron range), and at stress-intensity-factor ranges lower than the threshold for long cracks (millimeter range). Molecular dynamics simulations indicate that reversible plastic slip along the active crystallographic directions at the crack tip is responsible for advancing the crack during a fatigue cycle. In the case of single or double plastic slip localization at the crack tip, a typical Mode I fatigue crack deviates along a slip band, resulting in a mixed Mode I + Mode II crack-growth mechanism. For crystal orientations characterized by multiple slip systems concomitantly active at the crack tip, the crack advance mechanism is characterized by nanovoid nucleation in the high-density nucleation region ahead of the crack tip and linkage with the main crack leading to crack extension.

In Situ Tensile Deformation and Residual Stress Measurement by Neutron Diffraction in Modified 9Cr-1Mo Steel

AbstractThe deformation behavior of monolithic modified 9Cr-1Mo (Grade 91) steel during uniaxial tensile loading was studied using the in situ neutron diffraction technique. The residual stress distribution across gas tungsten arc welds in the Grade 91 steel was measured by the time-of-flight neutron diffraction method using the SMARTS diffractometer at Lujan Neutron Scattering Center, Los Alamos National Laboratory. Grade 91 plates were welded using the gas tungsten arc welding (GTAW) technique. The load sharing by different grain orientations was observed during the tensile loading. The residual stresses along three orthogonal directions were determined at the mid-thickness, 4.35 and 2.35 mm below the surface of both the as-welded and post-weld heat-treated plates. The residual stresses of the as-welded plates were compared with those of the post-weld heat-treated plates. The post-weld heat treatment significantly reduced the residual stress level in the base metal, the heat-affected zone, and the weld zone. Vickers microhardness across the weld zone of the as-welded and post-weld heat-treated specimens was evaluated and correlated with the observed residual stress profile and microstructure.

Numerical simulation of silicon wafer warpage due to thin film residual stresses

Wafer warpage is one of the most important challenges in the fabrication of modern electronic devices. Other challenges include handling, tool faults, and misalignments and even wafer breakage. The wafer warpage translates into die warpage that has a remarkable impact on die pick, stack and attach. This paper describes the work performed to simulate the silicon wafer warpage as a function of the wafer thickness and the film stresses using the commercial finite element code ABAQUS. The model accounts for the silicon anisotropy to better simulate the deformation. The computed values of the warpage were compared with experimental data and showed good correlation. The numerical model developed can be used to better understand the relation between the film stress and the wafer warpage. Furthermore it can be used to predict the warpage based on the wafer thickness and the film stress, which can help mitigate the warpage by depositing films to reduce the overall wafer warpage.

Finite element modeling of a back grinding process for Through Silicon Vias

The optimization of grinding parameters for silicon wafers is necessary in order to maximize the reliability of electronic packages. This paper describes the work performed to simulate a back grinding process for Through Silicon Via (TSV) wafers using the commercial finite element code ABAQUS. The grinding of a TSV silicon wafer with a thickness of 120 μm mounted on a backing tape was simulated. The wafer was thinned to a thickness of 115.5 μm, by simulating the grinding with a diamond particle cutting through successive silicon and copper layers. The computed residual stresses induced in the wafer were compared with experimental values, and the plastic deformation in the simulated ground surface was compared with literature data and showed good correlation. The numerical model developed can be used to better understand the local grinding parameters in the TSV wafers and the effect of the of the copper vias on the wafer properties.

Numerical simulation of heat generation during the back grinding process of silicon wafers

The optimization of grinding parameters for silicon wafers is necessary in order to increase the reliability of electronic packages. Grinding is a mechanical process performed on silicon wafers during which heat is generated. The amount of heat generated affects the reliability of the wafer, and implicitly that of the final product. This paper describes the work performed to simulate the heat generated during a back grinding process for silicon wafers using the commercial finite element code ABAQUS. The grinding of a silicon wafer with a thickness of 60 μm mounted on a carrier wafer using bond adhesive material was simulated. The heat generated is caused by the friction between the grinding wheel and the backside of the silicon wafer. The computed temperature change due to friction in the wafer was compared with experimental and numerical values, and showed a good correlation. The numerical model developed can be used to better understand the local grinding temperature in the wafers and to estimate the effect of the grinding parameters on the temperature rise.

A Numerical Strip-Yield Model for the Creep Crack Incubation in Steels

A numerical strip-yield model was developed to simulate creep crack incubation in heat-resistant steels. The model is based on a formulation proposed by Newman (Newman, J. C., Jr., “A Crack-Closure Model for Predicting Fatigue Crack Growth under Aircraft Spectrum Loading,” Methods and Models for Predicting Fatigue Crack Growth under Random Loading, ASTM STP 748, J. B. Chang and C. M. Hudson, Eds., ASTM International, West Conshohocken, PA, 1981, pp. 53–84) for fatigue crack growth under variable amplitude loading. The time evolution of the plastic deformation ahead of a crack loaded in tension is modeled using the Norton law for secondary creep stage, and the primary and tertiary creep stages are neglected. The model assumes a pre-existing crack in a specimen and models the behavior of the material prior to the beginning of crack propagation due to creep loading. The evolution with time of the crack-tip plastic zone, crack-tip opening displacement, and yield strength in the plastic zone are computed at constant temperature for center crack panels. Comparison with two previous strip-yield models and experimental data is performed, and good correlation is obtained for several Cr-Mo-V steels. This approach to modeling creep crack incubation has the potential to be applied to other types of cracked specimens under constant or variable amplitude loading.

A Visco-hyperelastic Model for the Thermo-mechanical Behavior of Polymer Fibers

A visco-hyperelastic model for the thermo-mechanical behavior of polymer yarns is presented. The model assumes that the stress in a yarn during uniaxial deformation results from the superposition of strain rate hardening effects and the softening caused by filament damage. The filament damage accounts for the fracture of polymer chains and the failure of inter-chain bonds. The constitutive model was implemented in the finite element method as a 1D rope element, and was applied to the study of nylon 6.6 and Kevlar ® 29 behavior. Numerical simulations of fabrics subjected to ballistic impact were performed, and the model is shown to predict the fabric penetration resistance and the deformation characteristics during the dynamic event.