theoretical and applied fracture mechanIcs ELSEVIER Theoretical and Applied Fracture Mechanics 32(1999)15-25 www.elsevier.com/locate/tafmec Determination of mechanical properties of fiber-matrix interface from pushout test . Ye..K. Kaw Mechanical Engineering Department, Unirersity of South Florida, Tampa, FL 33620-5350, USA Abstract For ceramic matrix composites, the pushout test is the most widely used test for finding the two mechanical properties of the fiber-matrix interface-(1)the coefficient of friction and (2) the residual radial stress. Experimental measurements from the pushout test do not directly give the values of these two mechanical properties of the fiber- natrix interface, but need to be regressed to theoretical models. Currently, approximate theoretical models based on shear-lag analysis are used for regression. In this paper, the adequacy of the shear-lag analysis model in accurately inding the mechanical properties of the fiber-matrix interface is discussed. An elasticity solution of the pushout test based on boundary element method is developed. Regressing one set of available experimental data from a pushout test to both shear-lag analysis and boundary element method models gives values differing by 15% for the coefficient of friction but similar values for the residual radial stress Parametric studies were also conducted to show the difference between the shear-lag analysis and boundary element method results for factors such as fiber to matrix elastic moduli ratios, coefficient of friction and fiber volume fractions. 1999 Elsevier Science Ltd. All rights reserved 1. Introduction Since the early 1980s, several experimental tests, such as the pushout test, have been developed to Fracture toughness of ceramic matrix compos find the two mechanical properties of the fiber- ites(CMCs)is dependent and sensitive to the two matrix interface in ceramic matrix composites mechanical properties of fiber-matrix interface [1].(CMCs). In the pushout test, a composite is sliced namely, the coefficient of friction and the residual normal to the fiber direction and the specimen is radial stress. Hence, there is a need to find these placed on a platform with a hole as shown in properties accurately. Only if these two properties Fig. 1. A micro-indentor with a radius that is 60- are found accurately, can we have reliable quan- 90% of the radius of the fiber pushes on the fiber. tification of the correlation of the microstructure Generally, the pushout force on the fiber and the and the fracture toughness, and then only can we displacement on the surface of the fiber below the have better control of the composite behavior for matrix surface due to interfacial slip are measured onducting optimum and reliable design of ce- to construct a pushout force vs. displacement ramic matrix composite structures curve. The pushout force-displacement curve from the test is then regressed to a theoretical model of the test for determining the two mechanical properties of the fiber-matrix interface. So far, the Corresponding author. Tel. +1-813-974-5626: fax: +1-813. theoretical models used for regression are limited 974-3539: e-mail: kaw deng. usf.edu to shear-lag analysis (SLA). In this paper, we 0167-8442/99/. see front matter @1999 Elsevier Science Ltd. All rights reserved PI:S0167-8442(99)00022Determination of mechanical properties of ®ber±matrix interface from pushout test J. Ye, A.K. Kaw * Mechanical Engineering Department, University of South Florida, Tampa, FL 33620-5350, USA Abstract For ceramic matrix composites, the pushout test is the most widely used test for ®nding the two mechanical properties of the ®ber±matrix interface ± (1) the coecient of friction and (2) the residual radial stress. Experimental measurements from the pushout test do not directly give the values of these two mechanical properties of the ®ber± matrix interface, but need to be regressed to theoretical models. Currently, approximate theoretical models based on shear±lag analysis are used for regression. In this paper, the adequacy of the shear±lag analysis model in accurately ®nding the mechanical properties of the ®ber±matrix interface is discussed. An elasticity solution of the pushout test based on boundary element method is developed. Regressing one set of available experimental data from a pushout test to both shear±lag analysis and boundary element method models gives values di€ering by 15% for the coecient of friction but similar values for the residual radial stress. Parametric studies were also conducted to show the di€erence between the shear±lag analysis and boundary element method results for factors such as ®ber to matrix elastic moduli ratios, coecient of friction and ®ber volume fractions. Ó 1999 Elsevier Science Ltd. All rights reserved. 1. Introduction Fracture toughness of ceramic matrix compos￾ites (CMCs) is dependent and sensitive to the two mechanical properties of ®ber±matrix interface [1], namely, the coecient of friction and the residual radial stress. Hence, there is a need to ®nd these properties accurately. Only if these two properties are found accurately, can we have reliable quan￾ti®cation of the correlation of the microstructure and the fracture toughness, and then only can we have better control of the composite behavior for conducting optimum and reliable design of ce￾ramic matrix composite structures. Since the early 1980s, several experimental tests, such as the pushout test, have been developed to ®nd the two mechanical properties of the ®ber± matrix interface in ceramic matrix composites (CMCs). In the pushout test, a composite is sliced normal to the ®ber direction and the specimen is placed on a platform with a hole as shown in Fig. 1. A micro-indentor with a radius that is 60± 90% of the radius of the ®ber pushes on the ®ber. Generally, the pushout force on the ®ber and the displacement on the surface of the ®ber below the matrix surface due to interfacial slip are measured to construct a pushout force vs. displacement curve. The pushout force±displacement curve from the test is then regressed to a theoretical model of the test for determining the two mechanical properties of the ®ber±matrix interface. So far, the theoretical models used for regression are limited to shear±lag analysis (SLA). In this paper, we www.elsevier.com/locate/tafmec Theoretical and Applied Fracture Mechanics 32 (1999) 15±25 * Corresponding author. Tel.: +1-813-974-5626; fax: +1-813- 974-3539; e-mail: kaw@eng.usf.edu 0167-8442/99/$ - see front matter Ó 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 8 4 4 2 ( 9 9 ) 0 0 022-1