Modelling the deformation and failure processes occurring in polymer bonded explosives (PBX) and other energetic materials is of great importance for processing methods and lifetime storage purposes. Crystal debonding is undesirable since this can lead to contamination and a reduction in mechanical properties. An insensitive high explosive (PBX-1) was the focus of the study. This binary particulate composite consists of (TATB) filler particles encapsulated in a polymeric binder (KELF800). The particle/matrix interface was characterised with a bi-linear cohesive law, the filler was treated as elastic and the matrix as visco-hyperelastic. Material parameters were determined experimentally for the binder and the cohesive parameters were obtained previously from Williamson et al. (2014) and Gee et al. (2007) for the interface. Once calibrated, the material laws were implemented in a finite element model to allow the macroscopic response of the composite to be simulated. A finite element mesh was generated using a SEM image to identify the filler particles which are represented as a set of 2D polygons. Simulated microstructures were also generated with the same size distribution and volume fraction only with the idealised assumption that the particles are a set of circles in 2D and spheres in 3D. The various model results were compared and a number of other variables were examined for their influence on the global deformation behaviour such as strain rate, cohesive parameters and contrast between filler and matrix modulus. The overwhelming outcome is that the geometry of the particles plays a crucial role in determining the onset of failure and the severity of fracture in relation to whether it is a purely local or global failure. The model was validated against a set of uniaxial tensile tests on PBX-1 and it was found that it predicted the initial modulus and failure stress and strain well.

Particulate composites are found in a wide range of applications. Their heterogeneous microstructure affects their bulk behavior and structural performance, however tools for predicting this important structure-property relationship are still lacking. In this study, a numerical method that can provide predictions of the mechanical response of a particulate polymeric matrix composite as a function of volume fraction and particle mean diameter is presented. The work is derived for an alumina trihydrate filled poly(methyl methacrylate) but the methodology is generic and can be used for any particulate composite. Representative Volume elements are determined through images obtained from scanning electron microscopy. The model takes into account the possibility of failure through interface debonding as well as cracks through the matrix. The model predictions for the modulus and fracture strength of the composites are validated through independent experiments on the composite. The numerical results are also used to qualitatively explain the trends measured regarding the fracture toughness of the composites. Compared to other literature on particulate composites, our study is the first to report accurate stress-strain distributions as well as fracture predictions whilst all the necessary model parameters defining the failure criteria are all derived through independent experiments. This paves R. Zhang · J. Y. S. Li-Mayer · M. N. Charalambides (B) Department of Mechanical Engineering, Imperial College London, South Kensington, London SW7 2AZ, UK e-mail: m.charalambides@imperial.ac.uk the way for a relatively simple methodology for determining structure-property relationships in composites design, enabling smarter material utilization and optimal mechanical properties.

A rheological constitutive model is required to characterize the behavior of a nitrocellulose-based material used as a binder in polymer bonded explosives. The behavior of the binder is extremely important as it heavily influences the mechanical response of the polymer composite; this is due to the binder having stiffness five orders of magnitude lower than the stiffness of the explosive crystals. Determination of the material model parameters is not straightforward; a constitutive law that will capture the pronounced time-dependent, temperature-dependent, and highly non-linear, large deformation response of this material is required. In this study, the material properties of the binder are determined using constant shear strain rate, shear stress relaxation, and monotonic tensile test results obtained over a wide range of temperature and strain rates. A visco-hyperelastic model is parameterized using the derived test data. In addition, recommendations are made regarding accurate data derived from rheological testing on such materials falling in the soft solid rather than the complex fluid domain.

Though a vast amount of literature can be found on modelling particulate reinforced composites and suspensions, the treatment of such materials at very high volume fractions (>90 %), typical of high performance energetic materials, remains a challenge. The latter is due to the very wide particle size distribution needed to reach such a high value of . In order to meet this challenge, multiscale models that can treat the presence of particles at various scales are needed. This study presents a novel hierarchical multiscale method for predicting the effective properties of elasto-viscoplastic polymeric composites at high . Firstly, simulated microstructures with randomly packed spherical inclusions in a polymeric matrix were generated. Homogenised properties predicted using the finite element (FE) method were then iteratively passed in a hierarchical multi-scale manner as modified matrix properties until the desired filler was achieved. The validated hierarchical model was then applied to a real composite with microstructures reconstructed from image scan data, incorporating cohesive elements to predict debonding of the filler particles and subsequent catastrophic failure.The predicted behaviour was compared to data from uniaxial tensile tests. Our method is applicable to the prediction of mechanical behaviour of any highly filled composite with a non-linear matrix, arbitrary particle filler shape and a large particle size distribution, surpassing limitations of traditional analytical models and other published computational models.

The suitability of an optimisation workflow for the determination of the mixed-mode cohesive zone model parameters using digital volume correlation (DVC) data and the inverse finite element method was examined. A virtual compression experiment of a cylinder with a spherical inclusion was modelled using the finite element method. A bilinear traction separation law with a linear mixed-mode relationship was used to describe the interfacial behaviour. Known mode I and mode II fracture energies, = 20 J/m2 and = 40 J/m2 and damage initiation stress, = 0.09 MPa, were used to generate a target composite debonding behaviour. An objective function,, determined based on the debonding behaviour measurable by DVC was chosen. A full factorial experiment was carried out for the four cohesive parameters and showed that correlation between fracture energies/ damage initiation stresses and is non-linear and discontinuous with multiple local minima. Optimisations initiated at the local minima identified from the full factorial experiment correctly determined the target cohesive fracture energies and damage initiation stresses.