Mechanical characterization of materials in fracture and fatigue with emphasis on the size effect

Resum

ABSTRACT This doctoral thesis presents model proposals for the material characterization both in static brittle fracture and fatigue failure. These models take into account the statistical size effect and the locally varying stress distributions, frequently encountered in test specimens, simultaneously. The statistical scatter of both failure stress for brittle materials and fatigue lifetime for components under cyclic loading is considered by deducing cumulative distribution functions (cdfs) following a three-parameter Weibull function. First, an evaluation method for 3- and 4-point bending test data obtained for brittle materials is proposed allowing to derive the three-parameter Weibull cdf of fracture stress referred to a uni-axially and uniformly tensioned surface element. For that purpose, an iterative fitting procedure is proposed and satisfactorily applied to experimental and simulated data sets. The results provided by this model are compared with those provided by a model proposed by Gross demonstrating good agreement between both. The difference between both methods lies in the simplification of the convergence procedure of the proposed model compared with Gross¿ model, besides, the former can be applied for the assessment of data obtained from different test geometries and types. Second, the proposed test evaluation method is extended to account for concurrent failure origins in brittle materials, e. g. in specimens that can fail both due to surface and edge defects. In this case, the cdfs of strength for surface and edge flaw populations are derived separately, both belonging to three-parameter Weibull families referred to an elementary surface area or elementary edge length, respectively. Its application to simulated data sets proved to be successful. As an additional parameter estimation technique for the strength characterization of brittle materials with concurrent failure modes a maximum likelihood estimator is proposed and applied to simulated 3-point bending test data. The estimated Weibull parameters are used to compute the cdfs of strength for specimens with different size whereby the confidence bounds are also provided using the bootstrap method. Further, the efficiency of the proposed method is corroborated by evaluating fracture data of 4-point bending tests on silicon carbide. Similar to the stress varying over the specimen length in uni-axial bending tests, the stress range in a uni-axially loaded fatigue specimen changes over its length if its radius is not constant. Thus, a parallelism between both cases is established allowing the parameter estimation technique proposed for brittle materials to be combined with the probabilistic fatigue model proposed by Castillo and Fernández-Canteli, which describes the S-N field by means of percentile curves, associated with constant failure probabilities. In this way, the fatigue characteristics of a certain material are deduced taking into account both the statistical size effect and the specimen geometry. As the estimated model parameters are referred to an elementary surface element, subject to a constant stress range, a comparison of fatigue data obtained on specimens with different geometries is facilitated. Furthermore, an extrapolation of the fatigue resistance to distinct specimen geometries is possible. To check the applicability of the proposed model, constant amplitude fatigue tests are carried out for two different materials, namely the low-alloy steel 42CrMoS4 and the aluminium alloy AlMgSi1. For each material unnotched specimens with three different geometries are tested. While the probabilistic fatigue model can be satisfactorily applied to each data set, the extrapolation from small specimen geometries towards larger ones results, sometimes, in a conservative estimation. Finally, a method is proposed to split the total fatigue lifetime into nucleation and propagation lifetime based on the frequency evolution during fatigue testing on resonant frequency testing machines.