Evolution Of Heterogeneous Deformation In Brittle Materials Under Dynamic Loading

Whether in daily life,engineering applications or in nature,the materials we contact or use always take on a heterogeneous internal structure.Owing to the heterogeneity in structure,the deformation of the material under external load is also heterogeneous.Stress/strain concentration occurs,and the damage of the material often start from these concentrated areas.The question of heterogeneity in material deformation has been extensively studied,but most of them focus on the degree of heterogeneity and the effect of heterogeneous deformation on the macroscopic properties of the material.Relatively speaking,the mesoscopic and microscopic mechanism of heterogeneity in material deformation and the evolution of heterogeneity during dynamic deformation are still scarce.This paper hopes to show the initiation and evolution process of heterogeneity in material deformation through experimental and theoretical exploration.Research in this paper is focused on brittle solid and particle materials.The structural heterogeneity of solid materials is manifested in open or closed microcracks with randomly distributed length and direction;the structural heterogeneity of the granular material is reflected by the assembly of particles and pores with various sizes and shapes.In this paper,the blocks with symmetrical oblique surfaces are added to the traditional dynamic and static loading device,namely the split Hopkinson pressure bar and the MTS material testing system,to conduct combined compression and shear loading on granite materials with different deformation rates and different loading paths.Using the high-speed photography and digital image correlation methods,the transverse tensile and maximum shear strain fields on the granite surface are obtained.Based on the two-dimensional strain field,the functions of strain evolution rate and damage nucleation rate are introduced to establish the relationship between the apparent deformation of the material and the internal crack growth.The statistical evolution equation of the strain field is derived to reveal the heterogeneity in deformation from the mesoscopic evolution mechanism.The granite material has obvious strain rate effect.It is found by the evolution equation that the high strain rate will cause the local strain evolution rate to accelerate and the damage nucleation rate to increase.Therefore,with the increasing of loading rate,the deformation rate of stress/strain concentrated region in granite is faster,more microcracks are activated,and the strain fields own high heterogeneity.The local strain amplitudes exhibit bimodal Weibull distribution feature.The first peak represents the quasi-elastic deformation of the matrix part in material,and the second peak represents the superposition of the quasi-elastic deformation and the crack nucleation/expansion induced deformation in the failure part.A large number of crack nucleation at high strain rates requires external loads to provide more energy,and the granite material owns a higher failure strength.At the same time,the granite material owns significant shear sensitivity.When there is shear component in the loading path,the local strain evolution rate and damage nucleation rate in the process of strain field evolution slightly increase,resulting in heterogeneous localization of strain field and crack nucleation expansion processes are more prone to occur,and accordingly the compression strength of the material is also reduced.In order to study the heterogeneous deformation of the material internal structure,the in-situ X-ray imaging technique was employed to capture the particle motion while using the miniature MTS material testing system and the miniature Hopkinson pressure bar to perform quasi-static and dynamic compression loading tests on boron carbide powder,respectively.The digital image correlation method are used to calculate the internal strain field of the powder.Under quasi-static compression,the compaction of the powder is holistic.When the particle stacking is loose,the compaction process is dominated by particle translation motion,which is presented as normal strain and the strain field is basically homogeneous;when the particle stacking is dense and real-time,and the compaction process is dominated by the particle rolling and sliding filling the pore volume,which is characterized by shear strain and the strain field exhibits a certain heterogeneity.Under dynamic compression,the compacted front in powder is observed,propagating along the loading direction with a velocity of 60-70 m/s.Before the front is the non-compaction region with small deformation and homogeneous strain field.The compaction region behind the front bears a highly heterogeneous strain field.Owing to the transformation process from compression to shear that occurs with the deformation rate increasing,the deformation of the compaction region is dominated by the particle rolling and sliding,and this rotation process also owns the characteristics of nucleation,growth and healing.An equivalent shear activation mechanism is proposed to describe the nucleation of dynamic compaction.A relaxation-diffusion model is established to simulate the process of dynamic compaction front propagation with a finite speed.When the powder stacking reaches a certain degree of compactness,the simulation effect is better.Both the heterogeneity in deformation and the increase in degree of particle rolling/sliding can promote the evolution of dynamic compaction.Compared to X-ray imaging,the X-ray diffraction method owns a higher resolution in the measurement of mesoscopic deformation of materials.In combination with X-ray imaging and diffraction techniques,dynamic uniaxial compression experiments were performed on boron carbide solids with two porosities using a miniature Hopkinson pressure bar.The particle adhesive force in the high-porosity solid is small,and after a transient deformation heterogeneity linearly increasing process under impact compression,the catastrophic damage occurs rapidly,and the failure strength is low.The low-porosity solid owns a high adhesive force.Although there are a large number of tensile and shear cracks nucleation,they cannot be connected into a crack network.The deformation heterogeneity increases linearly with a longer duration.After the intensity of diffraction peak decreasing and the peak cleaving process,dissociative damage caused by the penetration of the main crack occurs.Through the relaxation-diffusion model calculation,it is concluded that the propagation velocity of the failure surface in the low-porosity solid reaches about 2000 m/s,and although the material fracture degree increases entirely,the local regions own a slightly heterogeneous distribution.The brittle solid and particle materials studied in this paper are actually made up of particles,which differ only in the extent of adhesive forces between the particles.Based on the micromechanical mechanism of particles,the nonlinear elastic constitutive relation of the granular material can be obtained.By using the constitutive relation to calculate under hydrostatic pressure and one-dimensional strain state,the actual volume compressive modulus and shear modulus of the material under compression-shear coupling can be obtained,which is related to bulk density of the particles,the volumetric compressive modulus and shear modulus of the particles themselves.It is also controlled by the magnitude of volume and deviatory strain.The nonlinear elastic constitutive relation has obvious strain rate effect.When the deformation heterogeneity and shear deformation degree of the material increase,the overall stress increases faster with strain.In addition,the longitudinal and transverse wave velocity in granular material are also affected by the compression-shear coupling.The increase of shear component can cause the longitudinal wave velocity decreasing and the shear wave velocity increasing.However,when the shear component exceed a certain extent,the transverse wave velocity will appear to be reduced.