A new approach to fracture toughness analysis and its application to ABS polymers
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A new approach is proposed to analyze the fracture behavior with crack tip plasticity by the use of three independent measurements: Eo is the energy required per unit length of crack front to prepare the crack just before propagation; the Ef -curve is a plot of the energy required to produce a unit area of fractured surface versus the crack length; and the Ka-curve is a plot of the applied stress intensity factor KIapp versus the crack length. For ABS polymers, the prefracture energy Eo is 33 Jm^ 1 ; the Ef -curve is a horizontal line of 5.2 x 104 Jm~ 2 ; and the Ka curve has three different regions which depend on the development of the plastic zone during fracture.
I. INTRODUCTION Linear Elastic Fracture Mechanics (LEFM) is the most popular approach used in fracture toughness testing.1 From LEFM, the critical external crack driving force G relates to the critical stress intensity factor KIc by,
(1) where E is Young's modulus and 7 is the surface energy. But in reality, LEFM can be applied only to very brittle materials. The relationship is not correct if there is plastic deformation at the crack tip, since it is no longer true that the external work (other than elastic work) done at the loading points is equal to the irreversible work done by the Kj field at the crack tip to create new surfaces. With crack tip plasticity, the energy required to fracture the material has two parts. One is the so-called fracture toughness, which is defined as the energy needed to extend a unit area of fractured surface. The other is the energy needed to produce the plastic zone in front of the crack tip before the crack moves. So far, no fracture testing takes this part of the fracture barrier into account. All the available methods measure fracture toughness only. Besides the energy requirement, the external load needed to fracture the material is important also. That is the applied stress intensity factor KIapp, which may or may not be related to the fracture toughness. Kinloch and Shaw2 noticed that KIc alone was not enough to give the failure criteria of rubber-toughened epoxy; clearly more parameters were needed. In order to have a relatively complete characterization of the fracture behavior of the material, a method is suggested in this communication to measure the external energy and the load required to fracture the material. The experiments done on ABS polymers serve as an example to J. Mater. Res., Vol. 6, No. 6, Jun 1991
elucidate the concepts involved and to demonstrate the feasibility of this approach. A. Ef-curve and /Ca-curve The fracture energy Ef and the prefracture energy Eo are defined as follows, Ef = Eo =
-
B
dE(a) da
E(a = a0) B
(2) (3)
where a0 is the initial crack length, B is the sample thickness, and E(a) (see Fig. 1) is the total irreversible work required to propagate the crack to length a and is also the area enclosed between the initial loading line and the elastic unloading line of a crack of length a on the load-displacement diagram. Eo (see Fig. 1) is the energy required to produce the pla
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