anisotropic plasticity and failure prediction in wood ... - ANSYS Users

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ANISOTROPIC PLASTICITY AND FAILURE PREDICTION IN WOOD COMPOSITES Page 8 of 22 Size Effects The Weibull weakest link theory postulates that for brittle materials, larger specimens are more likely to fail at lower stresses due to the increased probability of a flaw in that larger specimen volume. Barrett (1974) found this to be true for the ultimate tension stress perpendicular-to-grain in Douglas fir. This concept was used to develop lumber strength design values for the Canadian standard for Engineering Design in Wood (O86.1, 1995). It has also been used to determine the strength of timber rivet connections listed in the standard (Foschi and Longworth, 1975). The probability of brittle failure based on a two-parameter Weibull distribution is a function of the stress distribution over the volume of material: file://C:\Documents%20and%20Settings\beh\Local%20Settings\Temp\~hhC936.htm 7/9/2002
ANISOTROPIC PLASTICITY AND FAILURE PREDICTION IN WOOD COMPOSITES Page 9 of 22 (5) where F is the probability of failure, V* is a reference volume, k is the shape parameter, m is the scale parameter associated with the reference volume, and is the stress (tension or shear, in any given direction or plane, respectively). The reference stress is based on experimental results shown in Table 1. (6) is the failure stress for a given probability of failure, p. It can be shown that failure occurs when the reference stress, *, occurring over volume V*, satisfies the following inequality which relates a variable state of stress over an arbitrary volume to the reference stress: (7) This form is similar to the Maximum Stress criterion where each stress is treated individually and stress interactions are assumed to have little or no effect. When the stress field is constant over a volume, equation (7) can be simplified to give the failure stresses for a given probability level, p: (8) where 1 and 2 are the strengths of specimens of volumes, V 1 and V 2 , respectively. This theory was implemented in ANSYS with a user-programmable command user01.f to execute the modified userac.f subroutine that calculated stresses in wood in the post-processor. The following algorithm for calculating the volume integral in equation (7) was carried out at each load-step in the post-processor to determine when or if failure occurred. At each load step, this algorithm was applied to each of the three normal tensile stresses and each of the three shear stresses. In this way, the governing mode of failure could be determined. The volume integral, I: (9) must be evaluated for each three-dimensional brick element (SOLID45) using Gaussian integration. Volume, V, in the global co-ordinate system (x,y,z), for each element is defined, in terms of the local (normalized) element co- ordinate system ( , , ): file://C:\Documents%20and%20Settings\beh\Local%20Settings\Temp\~hhC936.htm 7/9/2002
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anisotropic plasticity and failure prediction in wood ... - ANSYS Users

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