Thierry Hoc

Dislocation Mean Free Paths and Strain Hardening of Crystals

Predicting the strain hardening properties of crystals constitutes a long-standing challenge for dislocation theory. The main difficulty resides in the integration of dislocation processes through a wide range of time and length scales, up to macroscopic dimensions. In the present multiscale approach, dislocation dynamics simulations are used to establish a dislocation-based continuum model incorporating discrete and intermittent aspects of plastic flow. This is performed through the modeling of a key quantity, the mean free path of dislocations. The model is then integrated at the scale of bulk crystals, which allows for the detailed reproduction of the complex deformation curves of face-centered cubic crystals. Because of its predictive ability, the proposed framework has a large potential for further applications.

Polycrystal modelling of IF-Ti steel under complex loading path

Abstract Simple and complex loadings were performed on a IF-Ti steel in order to test different hardening laws. The different loading paths included uniaxial tension, plane strain, cyclic shear plane and plane strain tests followed by uniaxial tensile tests. Our aim was to determine the hardening law from these tests. For this purpose a polycrystalline self-consistent model was introduced. In this model an explicit concentration law and an intragranular behaviour based on the evolutions of physical parameters were proposed. Local objective frames were introduced to extend constitutive equations developed at small strains, to the finite strain framework. The identification of the physical parameters was performed thanks to an inverse method and led to values in good agreement with literature. For the different tests, macroscopic stresses and texture evolutions were computed and compared to experimental results. Initial and prestrain yield stresses surfaces were calculated. These different simulations pointed out for complex loading paths the necessity of an accurate description of the microplasticity mechanisms,in terms of slip systems, hardening matrix and evolution of dislocations densities on each slip system.

Mechanical and mineral properties of osteogenesis imperfecta human bones at the tissue level

Osteogenesis imperfecta (OI) is a genetic disorder characterized by an increase in bone fragility on the macroscopic scale, but few data are available to describe the mechanisms involved on the tissue scale and the possible correlations between these scales. To better understand the effects of OI on the properties of human bone, we studied the mechanical and chemical properties of eight bone samples from children suffering from OI and compared them to the properties of three controls. High-resolution computed tomography, nanoindentation and Raman microspectroscopy were used to assess those properties. A higher tissue mineral density was found for OI bone (1.131 gHA/cm3 vs. 1.032 gHA/cm3, p=0.032), along with a lower Youngs modulus (17.6 GPa vs. 20.5 GPa, p=0.024). Obviously, the mutation-induced collagen defects alter the collagen matrix, thereby affecting the mineralization. Raman spectroscopy showed that the mineral-to-matrix ratio was higher in the OI samples, while the crystallinity was lower, suggesting that the mineral crystals were smaller but more abundant in the case of OI. This change in crystal size, distribution and composition contributes to the observed decrease in mechanical strength.

Multiple scale modeling for cortical bone fracture in tension using X-FEM

We present a multiple scale method for modeling multiple crack growth in cortical bone under tension. The four phase composite Haversian microstructure is discretized by a Finite Element Method. The geometrical and mechanical bone parameters obtained by experiments mimic the heterogeneity of bone at the micro scale. The cracks are initiated at the micro scale where a critical elastic-damage strain driven criterion is met and are grown until complete failure in heterogeneous linear elastic media when a critical stress intensity factor criterion is reached. The cracks are modeled by the eXtended Finite Element Method. The simulations provide the global response at the macroscopic level and stress and strain fields at the microscopic level. The model emphasizes the importance of the microstructure on bone failure in assessing the fracture risk.

Microstructure and compressive mechanical properties of cortical bone in children with osteogenesis imperfecta treated with bisphosphonates compared with healthy children.

Osteogenesis imperfecta (OI) is a genetic disorder characterized by a change in bone tissue quality, but little data are available to describe the factors involved at the macroscopic scale. To better understand the effect of microstructure alterations on the mechanical properties at the sample scale, we studied the structural and mechanical properties of six cortical bone samples from children with OI treated with bisphosphonates and compared them to the properties of three controls. Scanning electron microscopy, high resolution computed tomography and compression testing were used to assess these properties. More resorption cavities and a higher osteocyte lacunar density were observed in OI bone compared with controls. Moreover, a higher porosity was measured for OI bones along with lower macroscopic Youngs modulus, yield stress and ultimate stress. The microstructure was impaired in OI bones; the higher porosity and osteocyte lacunar density negatively impacted the mechanical properties and made the bone more prone to fracture.

The deformation stage II of face-centered cubic crystals: Fifty years of investigations

Abstract This article critically reviews progress in the understanding of strain hardening during the deformation stage II of pure face-centered cubic crystals since its discovery in the mid-1950s. A wealth of models attempted explaining why stage II exhibits a linear slope on the base of specific dislocation configurations and interactions associated with short- or long-range internal stresses. Slip trace observations and more recent investigations on dislocation avalanches led to the identification of intermittent elementary slip events that are now investigated in terms of dislocation mechanisms. Numerical estimates showed that the overcoming of junctions and locks accounts for most of the flow stress and the hardening rate, as assumed by the present forest models. A multiscale analysis of stage II is outlined with emphasis on the modeling of dislocation mean free paths by dislocation dynamics simulations.

Predictive model for tensile strength of pharmaceutical tablets based on local hardness measurements

In the pharmaceutical field, tablets are the most common dosage forms for oral administration. During the manufacture of tablets, measures are taken to assure that they possess a suitable mechanical strength to avoid crumbling or breaking when handling while ensuring disintegration after administration. Accordingly, the tensile strength is an essential parameter to consider. In the present study, microscopic hardness and macroscopic tensile strength of binary tablets made from microcrystalline cellulose and caffeine in various proportions were measured. A relationship between these two mechanical properties was found for binary mixture. The proposed model was based on two physical measurements easily reachable: hardness and tablet density. Constants were determined from the two extreme compositions of this given system. This model was validated with experimental results, and a comparison was made with the one developed by Wu et al. (2005). Both models are relevant for this studied system. Nonetheless, with this model, the tablet tensile strength can be connected with a tablet characteristic at microscopic scale in which porosity is not needed.

Viscoelastic properties of rabbit osteoarthritic menisci: A correlation with matrix alterations

The aim of this study was to evaluate the effect of early osteoarthritis (OA) on the viscoelastic properties of rabbit menisci and to correlate the mechanical alterations with the microstructural changes. Anterior Cruciate Ligament Transection (ACLT) was performed in six male New-Zealand White rabbits on the right knee joint. Six healthy rabbits served as controls. Menisci were removed six weeks after ACLT and were graded macroscopically. Indentation-relaxation tests were performed in the anterior and posterior regions of the medial menisci. The collagen fibre organization and glycosaminoglycan (GAG) content were assessed by biphotonic confocal microscopy and histology, respectively. OA menisci displayed severe macroscopic lesions compared with healthy menisci (p=0.009). Moreover, the instantaneous and equilibrium moduli, which were 2.9±1.0MPa and 0.60±0.18MPa in the anterior region of healthy menisci, respectively, decreased significantly (p=0.03 and p=0.004, respectively) in OA menisci by 55% and 57%, respectively, indicating a global decrease in meniscal stiffness in this region. The equilibrium modulus alone decreased significantly (p=0.04) in the posterior region, going from 0.60±0.18MPa to 0.26±012MPa. This induced a loss of tissue elasticity. These mechanical changes were associated in the posterior region with a structural disruption of the superficial layers, from which the tie fibres emanate, and with a decrease in the GAG content in the anterior region. Consequently, the circumferential collagen fibres of the deep zone were dissociated and the collagen bundles were less compact. Our results demonstrate the strong meniscal modifications induced by ACLT at an early stage of OA and highlight the relationship between structural and chemical matrix alterations and mechanical properties.

Microscale mechanical and mineral heterogeneity of human cortical bone governs osteoclast activity

Human cortical bone permanently remodels itself resulting in a haversian microstructure with heterogeneous mechanical and mineral properties. Remodeling is carried out by a subtle equilibrium between bone formation by osteoblasts and bone degradation by osteoclasts. The mechanisms regulating osteoclast activity were studied using easy access supports whose homogeneous microstructures differ from human bone microstructure. In the current study, we show that human osteoclasts resorb human cortical bone non-randomly with respect to this specific human bone microstructural heterogeneity. The characterization of this new resorption profile demonstrates that osteoclasts preferentially resorb particular osteons that have weak mechanical properties and mineral contents and that contain small hydroxyapatite crystals with a high carbonate content. Therefore, the influence of human bone microstructure heterogeneity on osteoclast activity could be a key parameter for osteoclast behaviour, for both in vitro and clinical studies.

Contribution of collagen and elastin fibers to the mechanical behavior of an abdominal connective tissue

The linea alba is a complex structure commonly involved in hernia formation. Knowledge of its mechanical behavior is essential to design suitable meshes and reduce the risk of recurrence. The aim of this study was to investigate the relationships between the mechanical properties of the linea alba and the organization of collagen and elastin fibers. For that purpose, longitudinal and transversal samples were removed from four porcine and three human linea alba, to perform tensile tests under a biphotonic confocal microscope, in each direction. Microscopic observation revealed a tissue composed of two layers, made of transversal collagen fibers in the dorsal side and oblique collagen fibers in the ventral side. This particular architecture led to an anisotropic mechanical behavior, with higher stress in the transversal direction. During loading, oblique fibers of the ventral layer reoriented toward the tensile axis in both directions, while fibers of the dorsal layer remained in the transversal direction. This rotation of oblique fibers progressively increased the stiffness of the tissue and induced a non-linear stress-stretch relation. Elastin fibers formed a layer covering the collagen fibers and followed their movement, suggesting that they ensure their elastic recoil. All of these results demonstrated the strong relationships between the microstructure and the mechanical behavior of the linea alba.