Toughening criteria

Fond et al. [84] developed a numerical procedure to simulate a random distribution of voids in a definite volume. These simulations are limited with respect to a minimum distance between the pores equal to their radius. The detailed mathematical procedure to realize this simulation and to calculate the stress distribution by superposition of mechanical fields is described in [173] for rubber toughened systems and in [84] for macroporous epoxies. A typical result for the simulation of a three-dimensional void distribution is shown in Fig. 40, where a cube is subjected to uniaxial tension. The presence of voids induces stress concentrations which interact and it becomes possible to calculate the appearance of plasticity based on a von Mises stress criterion. 

The criterion was chosen since the toughening mechanism of CTPnBA/ Epon 828 systems was expected to be effective with this resin ratio range, based on CTBN rubber studies (10.14). The results suggested that the upper limiting molecular weight for the solubility of CTPnBA in Epon 828 was around Mn = 4400. 

Wu, S. (1985) Phase structure and adhesion in pol5mier blends a criterion for rubber toughening, Polymer, 26, 1855-1863. 

Wu, S. (1988) A generalized criterion for rubber toughening the critical matrix ligament thickness, J. Appl. Polymer Sci., 35, 549-561. 

Williams G, Watts DC (1970) Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function. Trans Faraday Soc 66 80-85 Williams ML, Landel RR, Ferry ID (1955) The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J Am Chem Soc 77 3701-3707 Wood LA (1958) Glass transition temperatures of copolymers. J Polym Sci 28 319-330 Wu SH (1985) Phase structure and adhesion in polymer blends a criterion for rubber toughening. Polymer 26 1855-1863... 

One of the serious difficulties in developing a quantitative description of toughening with elastomer particles is the lack of a suitable criterion for craze initiation. 

The mechanical and thermal properties of an in situ toughened silicon nitride material used to make a gas turbine combustor were experimentally measured. The location and nature of failure origins resulting from bend tests were determined with fractographic analysis. The measured Wei bull parameters were used along with thermal and stress analysis to determine failure probabilities of the combustor with the CARES design code. The effects of data censoring and fracture criterion were considered in the analysis. 

Maximum-stress-and-strain-based failure criteria were used by Harris and Adams (1984) to predict the failure of single lap joints. A nonlinear finite element analysis with an elasto-plastic material model for the adhesive and adherends was carried out. The selection of stressor strain-based failure criterion was based on the results of uniaxial tensile test results. For an un-toughened adhesive, a brittle failure was observed and a maximum stress criterion was used, while for a toughened adhesive, failure was ductile and a maximum-strain-based criteria was used. However, these criteria are difficult to implement when highly localized stress concentrations or stress singularities exist in an adhesive joint. 

Dompas D, Groeninckx G (1994) Toughening behavior of rubber-modified thermoplastic polymers involving very small rubber partides. 1. A criterion for internal rubber cavitation. Polymer 35 4743... 

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