By Yong Zhu, Alan T. Zehnder
Experimental and utilized Mechanics, quantity four of the Proceedings of the 2016 SEM Annual convention & Exposition on Experimental and utilized Mechanics, the fourth quantity of ten from the convention, brings jointly contributions to special components of analysis and engineering. the gathering offers early findings and case experiences on quite a lot of subject matters, including:
- Hybrid Experimental & Computational Techniques
- Advanced Experimental Mechanics Methods
- Integration of types & Experiments
- Soft Materials
- Education & learn in Progress
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Extra info for Experimental and Applied Mechanics, Volume 4: Proceedings of the 2016 Annual Conference on Experimental and Applied Mechanics
3 27 Calculating SIFs Using the Over-Deterministic Least-Squares Method In the over-deterministic LSM approach, the Westergaard’s stress function is used to determine the stress field ahead of the crack tip. This solution is written in the form of an infinite series expansion and it is not limited to the very near crack tip region. For the displacement components, the asymptotic equations are defined by : n n nn o n n n o þ ðÀ1Þn cos θ r n=2 κ cos θ À cos À 2 θ þ 2 2 2 2 2 2G n¼1 1 n nn o X Bn n=2 n n n n o À À ðÀ1Þn sin θ r κ sin θ À sin À 2 θ þ 2 2 2 2 2 2G n¼1 ð4:6Þ n n nn o n n n o þ ðÀ1Þn sin θ r n=2 κ sin θ þ sin À 2 θ À 2 2 2 2 2 2G n¼1 1 n nn o X Bn n=2 n n n n o À ðÀ1Þn cos θ r À Àκ cos θ À cos À 2 θ þ 2 2 2 2 2 2G n¼1 ð4:7Þ u¼ v¼ 1 X An 1 X An Particularly, the first terms of the series A1 and B1 are related to the mode I and mode II as follows: A1 ¼ B1 ¼ KI ð4:8Þ ð2π Þ1=2 K II ð4:9Þ ð2π Þ1=2 The displacements in Eqs.
1. In this work, we have chosen to project the displacement fields measured by DIC on a specific set of Williams’ series restricted to a mode I crack, using orders 0, 1 and 2. 6 Simulation Using A Crystal Plasticity Model The simulation of the experimental tensile test is performed using the finite element software Code_Aster. The phenomenological crystal plasticity law proposed by Me´ric and Cailletaud  has been chosen in this study. Intergranular cracked bicrystal has been modeling and meshed using quadratic quadrangles (Fig.
F II1 ðr 1 ; θ1 Þ ÁÁÁ 1 .. ⋮ ⋮ Á Á Á Àf IIm ðr M ; θM Þ ÁÁÁ 1 0 ÁÁÁ .. ÀgII1 ðr 1 ; θ1 Þ ÁÁÁ 0 .. ⋮ 1 ⋮ ÁÁÁ ÀgIIm ðr m ; θm Þ ÁÁÁ 1 ⋮ ⋮ 0 0 Ày1 3T 7 7 ⋮ 7 7 Àym 7 7 7 x1 7 7 7 7 ⋮ 5 ð4:15Þ xm Therefore, by using the least squares method to solve Eq. 12), the unknown parameters are determined as: h iÀ1 ½Δ ¼ ½CT Á ½C Á ½CT Á ½U ð4:16Þ To extract the crack tip location, the following methodology is adopted. First, an estimate of the crack tip position is located using the DIC image at the maximum load applied in the loading cycle.
Experimental and Applied Mechanics, Volume 4: Proceedings of the 2016 Annual Conference on Experimental and Applied Mechanics by Yong Zhu, Alan T. Zehnder