The thesis explores the role of microstructural heterogeneity in solids on their macroscopic mechanical response and develops a stochastic modelling framework which accounts for the effects of such heterogeneity.
First, the response of unidirectional 3D-printed PLA was investigated, and compared to that of injection-moulded PLA, to highlight the role of microstructural heterogeneity. The heterogeneous 3D-printed material is orthotropic and characterised by a strong tension-compression asymmetry. The material is tougher when loaded in the extrusion direction than in the transverse direction. The response of this unidirectional 3D-printed heterogeneous material was compared to that of its homogeneous counterpart (injection-moulded PLA), showing that manufacturing by 3D-printing imposed higher microstructural heterogeneity improves toughness.
A new damage measurement technique was then developed, with the inspiration from Continuous Stiffness Measurement (CSM) and studies on damage measurement of ductile metals. The measurement technique consists of small unloading/reloading cycles superimposed with a monotonically increasing load, when testing materials at laboratory scale. The stiffness of the specimen can be extracted from each cycle at various level of strain, allowing for extrapolation of the damage evolution in terms of stiffness degradation. Tests were performed on various materials including CFRP laminate, epoxy, 3D-printed PLA, Al sheet, Kanthal wire and sintered Ti to validate the feasibility of the proposed method. The interpretation of this information required a stochastic modelling framework, which was developed in the following.
The role of heterogeneity on the elastic-plastic material response was investigate. Monte Carlo analyses of the multiaxial loading of stochastic volume elements were conducted in ABAQUS/standard, to investigate the elastic-plastic response of isotropic heterogeneous random solids with non-uniform spatial distributions of mechanical properties. Simulations were conducted at different stress triaxiality and allow exploring the yield behaviour of the heterogeneous solids. It was shown that the variations of material properties induce strain localisation, necking instability, tension/compression asymmetry, size effects and plastic compressibility.
The effects of spatial heterogeneity of mechanical properties on the progressive damage mechanisms in tensile and fracture tests was then investigated. Both brittle and ductile solids cases were considered separately. It was found that heterogeneous solids are generally weaker than homogeneous solids and display a size-dependent response.
Finally, a stochastic modelling strategy was proposed, to predict the fracture response of a solid made from sintered Ti powder. The model was calibrated by stress versus strain histories measured in repeated monotonic uniaxial tension and compression tests, as well as damage measurements. Stochastic FE simulations were then performed to predict the measured fracture response of notched beams.