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].