A Probabilistic Approach to Assessing and Predicting the Failure of Notched Components

Abstract

This work presents a probabilistic model to evaluate the strength results obtained from an experimental characterisation program on notched components. The generalised local method (GLM) is applied to the derivation of the primary failure cumulative distribution function (PFCDF) as a material property (i.e., independent of the test type, load conditions and specimen geometry selected for the experimental campaign), which guarantees transferability in component design. To illustrate the applicability of the GLM methodology, an experimental program is performed using specimens of EPOLAM 2025 epoxy resin. Three different samples, each with a specific notch geometry, are tested. As a first scenario, a single assessment of each sample is obtained and the PFCDFs are used to perform cross predictions of failure. Some discrepancies are noticeable among the experimental results and cross-failure predictions, although they are within the expected margins. A possible reason for the disagreement can be assigned to the inherent statistical variability of the results and the limited number of tests per each sample. As a second scenario, a joint assessment of the three samples is performed, from which a unique PFCDF is provided, according to the GLM. In the latter case, a more reliable assessment of the experimental results from the geometry conditions is achieved, the suitability of the selected driving force is verified, and the transferability of the present material characterisation is confirmed.Materials 2019, 12, 4053 2 of 12 occur when the stress reaches the inherent strength (usually higher than the ultimate tensile strength of the material) at a distance of L/2 from the defect tip. In turn, the line method establishes that a fracture occurs when the average stress along a distance equal to 2L overcomes the inherent strength; the concept is similarly extended to the surface and volume methods.More recently, other models have emphasised the influence of external effects (e.g., temperature) on the fracture characterisation of notched-type elements, such as the notch master curve method [6] derived by applying the former master curve method to the failure analysis in the ductile-to-brittle transition in metals [7,8]. Finally, other approaches, based on the original TCD, have been presented during the few last years with the aim of including different effects, such as plasticity or constraints. Nevertheless, the vast majority of the above models only represent deterministic approaches.The significant and non-negligible scatter associated with fracture results has incited the development of probabilistic models. Some probabilistic models, similarly to certain deterministic models, have been set up to take into account external effects, such as temperature, as well as the notch influence as a combined effect acting on the apparent fracture toughness of metallic materials [9,10]. However, such models cannot guarantee the suitability of the selected parameter (driving force), to which the failure criterion is referred. Furtherm...

Fatigue Crack Growth from Notches: A Numerical Analysis

“…The radii considered for the notch in the present work (1-8 mm) are within the values proposed in the literature. Muñiz-Calvente et al [32] considered radii of 0.4, 1 and 2 mm, while Kolasangiani et al [33] studied strain ratcheting at notch roots with radius of 1.5, 4.5, and 7.5 mm. Ranganathan et al [4] considered radius of 3 mm in AA2024-T351 and of 1 mm in AA7749-T7951.…”

Probabilistic Assessment of Fracture Toughness of Epoxy Resin EPOLAM 2025 Including the Notch Radii Effect

“…Global and local methodologies, so denoted in allusion to the way in which the failure criterion is determined, that is, as referred to a driving force representing the hazard of the critical condition or the concatenation of local critical conditions, can be selected to characterize probabilistic fractures of polymeric notched materials [ 22 ]. The former is referred to as a unique driving force representative of the hazard of the critical condition being achieved, whereas the latter provides the global probability as a concatenation of local critical conditions.…”

Special Issue: Probabilistic Mechanical Fatigue and Fracture of Materials

“…Form the early efforts of calculating the influence of the stress distribution on the stress intensity factor, to present times, several researchers have proposed different methodologies for fracture characterization of notched specimens, with almost all of them being deterministic. However, the significant and non-negligible scatter associated with fracture results must be addressed by means of suitable probabilistic approaches, such as the proposal by Muñiz-Calvente et al [2]. This proposed methodology, based on the so-called generalized local model (GLM), allows for the primary failure cumulative distribution function (PFCDF) to be derived as a material property, that is, being independent of the test type, load conditions and specimen geometry.…”