Abstract
Considering that the correct quantification of fatigue damage involves two load parameters, the available load ratio data on polymeric materials are analyzed. It is shown that crack growth can be characterized by two parameters, ΔK and Kmax, without the need for any crack closure concept. The crack growth rates, starting from the threshold can be represented by the L-shaped curves in the ΔK-Kmax plane defining two limiting variables, ΔK* and Kmax*. Crack growth trajectory maps for various materials are developed by plotting ΔK* versus Kmax*, as a function of crack growth rate. The trajectory defines the crack growth resistance curve providing a measure of material resistance to increasing crack tip driving forces.
Keywords: Fatigue Crack Growth, Polymeric materials, Viscoelastic deformation, Crack growth by Crazing.
1. Introduction :
Fatigue requires two load parameters for quantification, as Gerber [1] and Goodman [2] recognized more than a hundred years ago. For S-N fatigue, stress amplitude and mean stress have been used. Fatigue S-N data are conveniently presented in the form of Haigh Diagrams in handbooks [3]. Of the five parameters, stress range (Δσ), maximum stress (σmax), mean stress (σmean), minimum stress (σmin), and load ratio (R), only two are independent. The rest of the parameters can be expressed in terms of the two. More importantly, at least two parameters are needed to quantify the fatigue damage correctly.
Two-load parameter requirement is also essential for the analysis of the fatigue crack growth (FCG). Still, this aspect has been ignored since Elber proposed the plasticity-induced crack closure concept in 1970 [4]. Subsequently, other forms of crack closure, such as oxide-induced, roughness-induced, etc., have been introduced to analyze the FCG data in different materials [5].
Note, however, that the crack closure is an extrinsic parameter and is not a substitute for the intrinsic two parametric requirements to quantify fatigue damage. If crack closure is present, it forms a third parameter that should be considered for FCG. Plasticity-induced crack closure was originally proposed for plane stress conditions by Budiansky and Hutchinson [6]. However, it was later extended to analyze the FCG data under plane strain conditions with some adjustable parameters, Newman et al. [7,8]. There are thousands of papers in the literature correlating the R-ratio effects of FCG using the crack closure concept. Using the dislocation theory [9], we have shown that plasticity under plane stain conditions does not contribute to crack closure, or its contribution is very minimal to account for the R-ratio effects. There was a follow-up discussion on this subject with Prof. Pippan’s group [10-13]. The fact remains, however, that crack closure was originally proposed for plane stress conditions [6]. In addition, we have shown that for S-N fatigue, fatigue can be represented better in terms of σmax and Δσ for a given number of cycles to failure, NF [14]. This representation is a modification of the familiar Haigh diagram for fatigue, where the data is generally expressed in terms of σmean and Δσ. Similarly, we have shown that the corresponding two parameters for FCG are Kmax and ΔK [16]. These concepts were applied to analyze FCG in metals, alloys, and their composites. In this paper, we extend the analysis to FCG in polymers to show the applicability of the two-parametric nature of fatigue even though they deform differently from metals and alloys [17].