Inversion Study On Stiffness Coefficients Of Fiber Reinforced Composites

Fiber reinforced composites are widely used in aerospace,vehicle engineering,wind power and other fields because of their excellent mechanical properties.Because the accuracy of composite structure simulation design highly depends on the accuracy of material constitutive parameters,engineers must carry out a large number of material standardization tests.Generally,unidirectional fiber reinforced composite exhibit orthotropic mechanical properties,with four independent in-plane stiffness coefficients Q₁₁,Q₂₂,Q₁₂and Q₆₆,corresponding to engineering elastic constants E₁,E₂,ν₂₁ and G₁₂.According to the existing testing standards of composite,at least three tests are required to fully obtain the above parameters.In order to overcome the shortcomings of the above standard tests,such as high cost,cumbersome process and difficult measurement of shear modulus,a new test scheme is developed based on the virtual fields method（VFM）.By prefabricating notches on both sides of the standard tensile specimen to excite the specimen to generate uneven strain fields,all four stiffness coefficients in the composite plane can be identified by one uniaxial tensile test.Firstly,the basic principle of VFM is introduced,and the special virtual fields formula for in-plane stiffness coefficients identification of orthotropic materials is deduced,which is solved by anti-noise optimization strategy.On this basis,the calculation program of VFM is compiled.Then,in order to induce the specimen to produce uneven strain fields and provide sufficient parameters inversion information,the idea of prefabricating V-notch on both sides of the tensile specimen is proposed.The design of specimen geometry is realized by using Python script and commercial finite element software ABAQUS.That is,batch modeling and analysis within the design range of each geometric parameters of the specimens and then substituting the generated ideal data of strain fields into the VFM for inversion calculation.Comparing the results with the material parameters input by finite element method to calculate the inversion error,and determining the best geometry of the specimen under the condition of minimum error.Finally,the method proposed in this paper is verified by experiments.The engineering elastic constants of glass fiber composites are measured through standardized tests,and then transformed into four in-plane stiffness coefficients as the reference values for VFM test verification.In order to ensure the repeatability of the method,five groups of the same VFM tests were carried out.The full field strain of the specimen surface was measured by Digital Image Correlation（DIC）.The influence of the deformation degree of the specimen on the inversion results is discussed,and the loading level suitable for parameter identification is determined.The experimental results show that the relative errors of Q₁₁,Q₂₂,Q₁₂ and Q₆₆ are0.508%,-0.945%,5.157%and-0.652%respectively,which proves the effectiveness of this method.