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Understanding how nanoparticles deform under compression is not only of scientific importance, but also has practical significance in various applications such as tribology, nanoparticle-based probes, and dry grinding of raw materials. In this study, we conducted compression tests on model brittle glassy nanoparticles using molecular dynamics simulations. We found that during the early stages of plastic deformation, shear bands formed in a similar pattern regardless of nanoparticle size. However, as the deformation continued, dominant cracks emerged in large nanoparticles while being suppressed in smaller ones. This size-dependent brittle to ductile transition can be explained by a simple model based on Griffith's theory. We also investigated the effect of surface stress state on fracture using thermally tempered nanoparticles. We observed that the presence of compressive surface stress strengthened the nanoparticle by suppressing crack formation, even when a pre-notch was present. On the other hand, tensile surface stress had the opposite effect. Interestingly, nanoparticles with both tensile and compressive surface stress promoted shear deformation, which could potentially compromise the mechanical performance of tempered glass despite delayed crack formation.
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Micromechanics based discrete damage model with multiple non-smooth yield surfaces: Theoretical formulation, numerical implementation and engineering applications
The discrete damage model presented in this paper accounts for 42 non-interacting crack microplanes directions. At the scale of the representative volume element, the free enthalpy is the sum of the elastic energy stored in the non-damaged bulk material and in the displacement jumps at crack faces. Closed cracks propagate in the pure mode II, whereas open cracks propagate in the mixed mode (I/II). The elastic domain is at the intersection of the yield surfaces of the activated crack families, and thus describes a non-smooth surface. In order to solve for the 42 crack densities, a Closest Point Projection algorithm is adopted locally. The representative volume element inelastic strain is calculated iteratively using the Newton–Raphson method. The proposed damage model was rigorously calibrated for both compressive and tensile stress paths. Finite element method simulations of triaxial compression tests showed that the transition between brittle and ductile behavior at increasing confining pressure can be captured. The cracks’ density, orientation, and location predicted in the simulations are in agreement with experimental observations made during compression and tension tests, and accurately show the difference between tensile and compressive strength. Plane stress tension tests simulated for a fiber-reinforced brittle material also demonstrated that the model can be used to interpret crack patterns, design composite structures and recommend reparation techniques for structural elements subjected to multiple damage mechanisms.
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- Award ID(s):
- 1552368
- PAR ID:
- 10211028
- Date Published:
- Journal Name:
- International Journal of Damage Mechanics
- Volume:
- 27
- Issue:
- 5
- ISSN:
- 1056-7895
- Page Range / eLocation ID:
- 611 to 639
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Understanding how nanoparticles deform under compression not only is of scientific importance but also has practical significance in various applications such as tribology, nanoparticle-based probes, and the dry grinding of raw materials. In this study, we conducted compression tests on model brittle glassy nanoparticles using molecular dynamics simulations. We found that during the early stages of plastic deformation, shear bands formed in a similar pattern regardless of the nanoparticle size. However, as the deformation continued, dominant cracks emerged in large nanoparticles while being suppressed in smaller ones. This size-dependent brittle-to-ductile transition can be explained by a simple model based on Griffith's theory. We also investigated the effect of the surface stress state on fracture using thermally tempered nanoparticles. We observed that the presence of compressive surface stress strengthened the nanoparticle by suppressing crack formation, even when a pre-notch was present. On the other hand, tensile surface stress had the opposite effect. Interestingly, nanoparticles with both tensile and compressive surface stress promoted shear deformation, which could potentially compromise the mechanical performance of tempered glass despite delayed crack formation.more » « less
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ABSTRACT Strongly anisotropic geomaterials, such as layered shales, have been observed to undergo fracture under compressive loading. This paper applies a phase‐field fracture model to study this fracture process. While phase‐field fracture models have several advantages—primarily that the fracture path is not predetermined but arises naturally from the evolution of a smooth non‐singular damage field—they provide unphysical predictions when the stress state is complex and includes compression that can cause crack faces to contact. Building on a recently developed phase‐field model that accounts for compressive traction across the crack face, this paper extends the model to the setting of anisotropic fracture. The key features of the model include the following: (1) a homogenized anisotropic elastic response and strongly anisotropic model for the work to fracture; (2) an effective damage response that accounts consistently for compressive traction across the crack face, that is derived from the anisotropic elastic response; (3) a regularized crack normal field that overcomes the shortcomings of the isotropic setting, and enables the correct crack response, both across and transverse to the crack face. To test the model, we first compare the predictions to phase‐field fracture evolution calculations in a fully resolved layered specimen with spatial inhomogeneity, and show that it captures the overall patterns of crack growth. We then apply the model to previously reported experimental observations of fracture evolution in laboratory specimens of shales under compression with confinement, and find that it predicts well the observed crack patterns in a broad range of loading conditions. We further apply the model to predict the growth of wing cracks under compression and confinement. Prior approaches to simulate wing cracks have treated the initial cracks as an external boundary, which makes them difficult to apply to general settings. Here, the effective crack response model enables us to treat the initial crack simply as a nonsingular damaged zone within the computational domain, thereby allowing for easy and general computations.more » « less
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The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the “sprain,” as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ( ) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.more » « less
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In this study, deformation and failure mechanisms of mineralized tissue (bone) were investigated both experimentally and computationally by performing diametral compression tests on millimetric disk specimens and conducting finite element analysis in which a granular micromechanics-based nonlinear user-defined material model is implemented. The force–displacement relationship obtained in the simulation agreed well with the experimental results. The simulation was also able to capture location of the failure initiation observed in the experiment, which is inside out from the hole along the loading axis. Furthermore, propagation of micro-sized cracks into failure was observed both in the experiment using simultaneous slow-motion microscopy imaging and in the simulation analyzing the local distortion and local volume change within the specimen. The anisotropy evolution was found to be significant around the hole along the loading axis by evaluating the anisotropy index computed using finite element results. In conclusion, this work revealed that the prediction capability of granular micromechanics-based user-defined nonlinear material model (UMAT) is promising considering the match between the results and observations from the physical experiment and finite element analysis such as force–displacement relationship and failure initiation/pattern. This work has also shown that the tensile damage and failure of mineralized tissues can be characterized using diametral compression (split tension) test.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1177/1056789517695872
