D. Koch et aL Composites Science and Technology 68(2008)1165-1172 three different failure modes occur. In 0%/90 orientation Unloading-reloading cycles reveal inelastic strain and stiff- high strength at about 400 MPa is measured in tensile ness reduction which are a result of the increasing damage mode and the fracture is characterized by fiber failure. processes in the matrix while the acoustic emission signal Under compression the composite fails due to fiber buck- give a qualitative proof of the ongoing damage processes ling. As the composite is extremely shear sensitive with a The experimentally derived macroscopic properties of shear strength of about 35 MPa shear failure of the com- WMC under tensile, shear, and compressive loading are posite is observed when shear stresses are superimposed. used to establish a finite element model which allows This happens in the off-axis tension and compression tests the prediction of mechanical behavior of these composites with increasing angle between fiber and loading orientation Fig. 8). The model is based on continuum damage resulting in a reduced strength. The experimental data are mechanics and allows the separate calculation of inelastic to be calculated using the failure criterion from Hill with deformation and stifness degradation inducing yield sur the assumption that the composite behaves symmetrically faces and damage surfaces with the assumptions of iso- and using tensile, compressive and pure shear strength val- tropic hardening and associated flaw rules. The ues as input data. Details are described elsewhere [ll] hardening functions, which calculate inelastic deforma tion and stifness reduction are coupled by using the same 6. Modeling of mechanical behavior equivalent stress. The implementation of the model into a finite element code in marc allows the calculation of As already mentioned the damage and failure mecha- the stress-strain behavior of composites loaded with dif- nisms of WMC cannot be described sufficiently by a micro- ferent angles between fiber orientation and loading direc mechanical approach as in general large volume failure tion [9, 11, 14]. occurs. To understand the damage evolution pure tensile and pure shear tests have been performed with unload- 7. Model application for notched specimens ing-reloading cycles. Under these loading conditions the material response is dominated either by the fibers or by The established Fe model is used to predict the fail the matrix(Fig. 7). Under pure tensile mode the stress- behavior of complex shaped samples. As an example strain curve remains almost linear-elastic and almost no DEn (double end notch) specimens are investigated under residual strain is observed during unloading cycles 0/900 and+45/-45 loading conditions( Fig 9).Further (Fig. 7a). However, acoustic emission signals show that more the ligament width and accordingly the notch length at high stresses damage occurs which can be attributed to were varied. With increasing ligament width a slight matrix crack evolution and propagation. Under shear load- decrease of strength is measured in case of on-axis loading ing a strong nonlinear behavior is observed(Fig. 7b).( Fig. 10a). This width effect is also observed at unnotched Experiments Input data Shear Strain [5] FE-Implementatio MARC §直 Prediction of material ' s properties stress-strain curve strength Fig 8. Schematic flow diagram of modeling the inelastic deformation and damage of weak matrix composites.three different failure modes occur. In 0/90 orientation high strength at about 400 MPa is measured in tensile mode and the fracture is characterized by fiber failure. Under compression the composite fails due to fiber buck￾ling. As the composite is extremely shear sensitive with a shear strength of about 35 MPa shear failure of the com￾posite is observed when shear stresses are superimposed. This happens in the off-axis tension and compression tests with increasing angle between fiber and loading orientation resulting in a reduced strength. The experimental data are to be calculated using the failure criterion from Hill with the assumption that the composite behaves symmetrically and using tensile, compressive and pure shear strength val￾ues as input data. Details are described elsewhere [11]. 6. Modeling of mechanical behavior As already mentioned the damage and failure mecha￾nisms of WMC cannot be described sufficiently by a micro￾mechanical approach as in general large volume failure occurs. To understand the damage evolution pure tensile and pure shear tests have been performed with unload￾ing–reloading cycles. Under these loading conditions the material response is dominated either by the fibers or by the matrix (Fig. 7). Under pure tensile mode the stress– strain curve remains almost linear-elastic and almost no residual strain is observed during unloading cycles (Fig. 7a). However, acoustic emission signals show that at high stresses damage occurs which can be attributed to matrix crack evolution and propagation. Under shear load￾ing a strong nonlinear behavior is observed (Fig. 7b). Unloading–reloading cycles reveal inelastic strain and stiff- ness reduction which are a result of the increasing damage processes in the matrix while the acoustic emission signals give a qualitative proof of the ongoing damage processes. The experimentally derived macroscopic properties of WMC under tensile, shear, and compressive loading are used to establish a finite element model which allows the prediction of mechanical behavior of these composites (Fig. 8). The model is based on continuum damage mechanics and allows the separate calculation of inelastic deformation and stiffness degradation inducing yield sur￾faces and damage surfaces with the assumptions of iso￾tropic hardening and associated flaw rules. The hardening functions, which calculate inelastic deforma￾tion and stiffness reduction are coupled by using the same equivalent stress. The implementation of the model into a finite element code in MARC allows the calculation of the stress–strain behavior of composites loaded with dif￾ferent angles between fiber orientation and loading direc￾tion [9,11,14]. 7. Model application for notched specimens The established FE model is used to predict the failure behavior of complex shaped samples. As an example DEN (double end notch) specimens are investigated under 0/90 and +45/45 loading conditions (Fig. 9). Further￾more the ligament width and accordingly the notch length were varied. With increasing ligament width a slight decrease of strength is measured in case of on-axis loading (Fig. 10a). This width effect is also observed at unnotched Fig. 8. Schematic flow diagram of modeling the inelastic deformation and damage of weak matrix composites. 1170 D. Koch et al. / Composites Science and Technology 68 (2008) 1165–1172