Maximum Hydrostatic Stress Research Articles

In-situ studies on environmental degradation in Al 7075 in saltwater environment under tensile loading

Abstract We report the crack growth on peak aged Al 7075 under tensile loading in a saltwater environment to investigate whether hydrogen plays a role in the initiation and the subsequent growth of the crack. As the hydrostatic stress is at a maximum ahead of the notch, it has been speculated that hydrogen would diffuse to region of maximum hydrostatic stress and initiate the crack. An elastic-plastic finite element (FE) model is developed to determine the stress distribution around the circular notch at the edge of the plate. The crack growth was monitored using a camera attached with an optical microscope, and various regimes corresponding to hydrogen evolution, pit formation and growth, crack nucleation and initial growth and rapid crack growth leading to failure have been identified. We observe the crack was nucleated in a region associated with the highest hoop stress instead of the maximum hydrostatic stress from the base of a pit at the circular notch. We demonstrated the crack growth rate in a salt water environment is governed mostly by the dissolution of grain boundary MgZn2 precipitate, rather than the hydrogen induced decohesion mechanism.

A Mechanical Approach to the Growth Plate Behaviour and Chondrocytes Columns Organization

This study aims to explore the behaviour of mechanical stimuli and their effect on growth plate shape under different physiological scenarios and loading conditions. A linear elastic, isotropic, and homogeneous model was implemented to model the epiphyseal progressive ossification and the development of the secondary ossification centre. Results shed light on the role of mechanical stimulus, suggesting that maximum shear stress, hydrostatic stress, and von Mises Stress may contribute to the morphological changes of the growth plate. This model is a useful tool to improve orthopaedic therapies focused on pathologies that imply abnormal bone growth under abnormal mechanical conditions.

A standardizable approach for Tooth Flank Fracture

Ultrasonic scanning of large spiral bevel gears and the subsequent fracture analyses of early-stage tooth flank fractures imply a mode II crack initiation under surface-parallel, orthogonal shear stresses. An iteration of the Dang Van criterion is presented that focuses exclusively on surface-parallel material planes, yielding a standardizable approach for the study of tooth flank fracture in spiral bevel gears. It is shown that Dang Van’s shear stress amplitude and maximum hydrostatic stress along a surface-perpendicular path can adequately be described by the Hertzian orthogonal shear stress amplitude and Lang’s compressive residual stress. The fatigue properties along the same path are estimated from Thomas’ hardness model and augmented by ISO-inspired lifetime, size and conversion factors. The article closes with a comparison between the commonly used Witzig-Boiadjiev, Hertter-Wirth, DNV subsurface fatigue and the herein proposed, rationalized Dang Van criterion.

Anchorage effects of ligation and direct occlusion in orthodontics: A finite element analysis

Background and objectiveDuring orthodontic treatment, the figure-of-eight ligature and the physiological occlusion play an important role in providing anchorage effects. However, their effects on reaction forces of tooth and stress state in periodontal ligament (PDL) have not been quantitatively evaluated yet. In this study, we presented a finite element analysis process for simulating posterior molar ligature and direct occlusion during orthodontics in order to quantitatively assess their anchorage effects. MethodsA high precision 3D biomechanical model containing upper and lower teeth, PDL, brackets and archwire was generated from the images of computed tomographic scan and sophisticated modelling procedures. The orthodontic treatment of closing the extraction gap was simulated via the finite element method to evaluate the biomechanical response of the molars under the conditions with or without ligation. The simulations were divided into experimental and control groups. In the experimental group, orthodontic force of 1 N was first applied, then direct occlusal forces of 3 and 10 N were applied on each opposite tooth. While in the control group, occlusal forces were applied without orthodontic treatment. The tooth displacement, the stress state in the PDL and the directions of the resultant forces on each tooth were evaluated. ResultsIn the case of molars ligated, the maximum hydrostatic stress in the molars’ PDL decreases by 60%. When an initial tooth displacement of several microns occurs in response to an orthodontic force, the direction of the occlusal force changes simultaneously. Even a moderate occlusal force (3 N per tooth) can almost completely offset the mesial forces on the maxillary teeth, thus to provide effective anchorage effect for the orthodontics. ConclusionsThe proposed method is effective for simulating ligation and direct occlusion. Figure-of-eight ligature can effectively disperse orthodontic forces on the posterior teeth, while a good original occlusal relationship provides considerable anchorage effects in orthodontics.

Investigation of the fracture mechanism of level ice with extended finite element method

This paper investigates the fracture mechanism of level ice based on the extended finite element method by simulating collision scenarios between ice and a rigid ship structure. It is found the collision velocity and structure inclination affect the fracture mode through changing the deformation and stress distribution of the level ice. The overall response of the level ice is simulated with the transversely isotropic material model and cohesive zone model. The numerical model is verified with the data from a field test, which shows that the obtained ice load and size of the broken ices from numerical method are well consistent with the tested data. Two fracture modes of the level ice, bending and splitting, appear in the simulated cases. The bending crack is found to emerge from the top surface of the level ice and expand along the circumferential direction, and the splitting crack initiates at the bottom edge of the level ice and expands along the radial direction. Deformation and multiple stresses of level ice are analyzed, showing that the initial cracks for both fracture modes are related to the local tensile failure, and the location of the maximum tensile hydrostatic stress always coincides with the initial crack.

On the effects of texture and microstructure on hydrogen transport towards notch tips: A CPFE study

Hydrogen embrittlement is an important degradation mechanism affecting the lifetime of engineering components. The diffusion of hydrogen atoms into the metal lattice can be affected by the localized stresses that develop around service-induced flaws. In addition, the magnitudes of flaw tip stresses are affected by the flaw geometry, as well as the texture and microstructure of the metal. Microstructural effects can be significant, particularly in metals such as zirconium with a high degree of elastic and plastic anisotropy. This study uses a coupled diffusion-crystal plasticity finite element approach to conduct a comprehensive study on the redistribution of hydrogen atoms in the vicinity of service-induced flaws in zirconium polycrystals. The effects of texture, grain size, and notch tip geometry on the concentration of hydrogen atoms in the lattice sites are investigated. The results indicate that material texture can significantly affect the distribution of hydrogen atoms as well as the location of maximum hydrostatic stress and maximum hydrogen concentration. The modeled highly textured microstructures have connected regions of peak hydrogen concentration. It is shown that as the notch tip becomes sharper, the effects of texture on the hydrogen localization near the notch become less significant. It is also shown that with changing grain orientations, it is possible to move the location of peak hydrogen concentration away from the notch tip.

46 - Optimal Intrusive Force for a Periodontally Compromised Tooth: A Finite Element Analysis Strategy

The present study evaluated the optimal force for orthodontic intrusive mechanics of a tooth with different levels of periodontal support reduction using a finite element analysis (FEA) approach. An anatomical 3D model was constructed representing a second unirradicular premolar inserted into a maxillary bone segment. Based on the control model, three horizontal bone resorption conditions were simulated with alveolar bone height loss of 2 mm, 4 mm, and 6 mm (R2, R4, and R6, respectively). An 25 cN intrusive force was used for the two simulated mechanics: bilateral mini-implant intrusion and conventional intrusion. A root resorption risk index (RRRi) was calculated by dividing the maximum compressive hydrostatic stress in the periodontal ligament by the hydrostatic stress of the capillaries (4.7 kPa). It was assumed that the optimal intrusive force of reduced periodontal premolars was reached when the compressive hydrostatic stress distributions pattern of the reduced models was similar to those found in the control models of the corresponding mechanics. The FEA optimal force values for each model were compared with those obtained by the analytical formula (Force = stress x area). A linear trendline was observed between the control force reduction percentage and the bone loss height for both mechanics. For each millimeter of bone height loss, the control force had to be reduced by 9% for conventional intrusion, and by 8% for bilateral mini-implant intrusion. The root resorption risk index and the optimal intrusive force depends not only on the remaining root area with ligament support, but also on the intrusive mechanics used. The use of bilateral mini-implants in orthodontic intrusion reduced the external apical root resorption risk index and increased the optimal intrusive force. The proposed FEA strategy provided an easy, precise and feasible approach to suggest the optimum force in a clinical situation.

Hydrogen embrittlement of pearlitic steel in the presence of cracks: A kinematic fracture criterion based on the crack tip strain rate

This paper offers a kinematic fracture criterion for hydrogen embrittlement (or hydrogen assisted cracking) of cracked samples of high strength pearlitic steel tested at very different loading/straining rates under cathodic electrochemical conditions promoting hydrogen entry and diffusion into the specimens. The local strain rate at the crack tip (crack tip strain rate CTSR) is shown to be the relevant variable governing the hydrogen embrittlement process. Calculation of the local strain rate is carried out on the basis of the elastic displacement distribution in the vicinity of a crack tip in conditions of plain strain. A local reference length is chosen next to the crack tip, at a distance estimated from the fractographic results of the tests that show a zone microscopically affected by hydrogen. The other relevant variable in hydrogen assisted cracking is the depth of the maximum hydrostatic stress point, which is obtained by using approximate stress distributions in the vicinity of the crack tip in the elastic-plastic regime, or calculated as the asymptotic depth (for quasi-static tests) of the hydrogen affected area.

Numerical modeling of hydrogen embrittlement of pearlitic steel in the presence of blunt notches

This paper offers a numerical modeling of hydrogen embrittlement and notch tensile strength of high-strength pearlitic steel (supplied in the form of hot rolled bars) in the presence of blunt notches, by using the finite element method in order to determine how the notch depth influences the concentration of hydrogen in the steady-state regime for different loading values. Numerical results show that the maximum hydrostatic stress location (towards which hydrogen is directed by a mechanism of stress-assisted diffusion) shifts from the notch tip to the inner points of the specimen under increasing load, even reaching the sample axis for the most elevated levels of externally applied stress.

Study on ultra-high speed nano-grinding of monocrystalline copper with V-shaped diamond abrasive grains based on molecular dynamics method

The process of ultra-high-speed nano-grinding of V-grooves was studied by the molecular dynamics method. It was found that the phenomenon of unequal height on both sides of the V-shaped groove was affected by the rake angle of the abrasive grains. To further explore the mechanism of the influence, five kinds of V-shaped diamond abrasive grains with rake angles of −20°, −10°, 0°, 10° and 20° were used to grind monocrystalline copper, and the forming mechanism of the inconsistent height of the two sides of the V-shaped groove was analyzed in detail. In addition, the distributions of the maximum principal stress, maximum shear stress, hydrostatic stress, and von Mises stress in the grinding were calculated. Consequently, the positive rake grinding can obtain a V-shaped cross-section with a uniform height on both sides. Therefore, the V-shaped abrasive grains with a positive rake angle can be used to obtain a high-quality V-shaped groove.

Impact analysis of PEEK/ceramic/gelatin composite for finding behind the armor trauma

A ceramic-based armor system must arrest bullet penetration and dissipate a large amount of impact energy. Taking the total linear momentum transferred to the wearer of a ceramic armor as a measure of the behind-armor ballistic/blunt trauma (BABT), we study the effect on the BABT of adding a thin polyether-ether-ketone (PEEK) layer on the face of a Silicon Carbide (SiC) ceramic target impacted at normal incidence by a full metal jacket bullet traveling at a low velocity. A human torso is simulated by a block of ballistic gelatin. Three-dimensional non-linear large deformations of the system are numerically analyzed using the commercial finite element software ABAQUS/Explicit with the full integration rule to evaluate elemental matrices. Sensitivity tests are conducted with random samples generated by the Latin Hypercube Sampling technique to delineate the influence of the static yield stress, strain hardening, Young’s modulus and the mass density of the PEEK layer as well as of the shear modulus, the mass density and the maximum hydrostatic tensile stress of the ceramic on the BABT. It is found that reducing the acoustic mismatch between the PEEK and the ceramic increased the plastic energy dissipated in the ceramic. For normal impact at 180 m/s of a bullet having kinetic energy of 130 J, the 2 mm thick surface layer decreased the total peak normal force, the normal impulse transmitted, and the maximum pressure transferred from the SiC target to the gelatin layer by 19%, 18% and 32%, respectively. Simulations using a reduced integration rule significantly under-predict the final kinetic energy and the back face displacement of the bullet as compared to those using the full integration rule. For the 2 mm thick PEEK layer located on the top, the middle and the bottom of the SiC plate, the back face displacement is the least for the layer located in the middle but the BABT increased.

Hydrogen embrittlement and notch tensile strength of pearlitic steel: a numerical approach

This paper offers a numerical approach to the problem of hydrogen embrittlement and notch tensile strength of sharply notched specimens of high-strength pearlitic steel supplied in the form of hot rolled bars, by using the finite element method in order to determine how the notch depth influences the concentration of hydrogen in the steady-state regime for different loading values. Numerical results show that the point of maximum hydrostatic stress (towards which hydrogen is transported by a mechanism of stress-assisted diffusion) shifts from the notch tip to the inner points of the specimen under increasing load, with numerical evidence of an elevated inwards gradient of hydrostatic stress “pumping” hydrogen inside the sample.

A stress triaxiality based modified Liu–Murakami creep damage model for creep crack growth life prediction in different specimens

Liu–Murakami creep damage model is improved to predict the creep life of various cracked specimens. The modified creep damage law is implemented in the framework of extended finite element method (XFEM) for performing elasto-plastic creep crack growth simulations. Experiments show that the crack tip constraints vary from component to component which leads to variation in crack growth rates. A stress triaxiality function is introduced in the modified Liu–Murakami damage model to address the variation in crack growth rates. Moreover, a new definition of stress triaxiality (ratio of a linear combination of maximum principal stress and hydrostatic stress to von Mises stress) is proposed based on Leckie and Hayhurst failure criterion. The new definition of stress triaxiality is a key parameter in the prediction of time to failure. The modified Liu–Murakami creep damage model is used for the creep crack growth (CCG) simulations of several specimens under different loading conditions. Parametric studies are also performed to study the influence of various parameters on the CCG. Moreover, a combined framework of continuum damage mechanics and XFEM is used to predict the CCG life of a turbine blade. This work establishes that the modified Liu–Murakami creep damage law accurately predicts the creep life of cracked components under different constraint conditions.

Temperature dependent two-body abrasive wear of polycarbonate surfaces

During the lifetime of polycarbonate surfaces, which for example are used as helmets or protective eye visors, friction and abrasive wear may result from scratching or sliding cycles. Previous research showed that it is essential to understand the intrinsic mechanical response of the polymer in order to further investigate its frictional and wear response. The Eindhoven Glassy Polymer (EGP) model is a 3D elasto-viscoplastic constitutive model, developed to describe the intrinsic mechanical response of polymer glasses. Temperature is a crucial player in the intrinsic response and also plays a pivotal role in the resulting frictional response as tested via a single-asperity scratch test. In the current study, a finite element model is used to investigate the effect of temperature on the frictional response of polycarbonate and detect the onset of crack formation and wear initiation. The results show that temperature has a strong effect on the intrinsic response of the polymer, i.e. drop in yield stress and altered strain-hardening and strain-softening response. However, it has a minute effect on its frictional response, the simulation model is able to capture this response quantitively. In addition, cracks are observed experimentally at elevated temperature. A critical positive hydrostatic stress value is selected as a criterion for crack formation. It has been shown that at elevated temperatures the value of the maximum positive hydrostatic stress increases due to the altered intrinsic response of the material on one hand, and the increased adhesion between the tip and the polymer on the other hand.

Multiaxial fatigue of quenched and tempered U2 steel: Testing and fatigue life prediction

AbstractTension‐compression, tension‐tension, torsional, and 90° out‐of‐phase axial‐torsional fatigue tests were performed on a quenched and tempered U2 steel. All tests were conducted under force/torque control because macroscopic plastic strains were insignificant in the life range of interest (from 104 to 2 × 106 loading cycles). Stress‐based versions of the Fatemi‐Socie critical plane parameter and of the Smith‐Watson‐Topper parameter with a critical plane interpretation were evaluated using the experimental data. The Smith‐Watson‐Topper parameter was not able to correlate the test data. The Fatemi‐Socie method correlated most of the test data within factor‐of‐three boundaries. A modified Crossland invariant‐based parameter made of two interaction rules between the shear stress amplitude and the maximum hydrostatic stress, and of a definition of shear stress amplitude based on the maximum prismatic hull method, yielded fatigue life estimates in reasonable agreement with the experimental observations.

Hydrostatic stress as indicator for wear initiation in polymer tribology

Over the last two decades the study of friction has been an important topic in polymer tribology. The obtained knowledge about friction phenomena enables to take the next step towards understanding wear in polymers. When increasing the amount of local deformation in sliding friction experiments, the onset of failure is obtained, i.e. periodic cracks are initiated. Comparing the location of these cracks for a range of polymers with large differences in their intrinsic deformation response, suggests that different kinds of wear mechanisms are important. The relation between these mechanisms and the intrinsic properties are explained by the subtle interplay between intrinsic strain softening and strain hardening in the material. The critical locations for crack initiation are for polystyrene behind the indenter tip, at the centerline of the scratch, while for high-density polyethylene the cracks are initiated in the bow wave in front of the indenter. In finite element scratch simulations, the position of the maximum hydrostatic stress appears to be identical to the experimentally observed crack location. This suggests that crack initiation is related to a critical positive hydrostatic stress, which is known to be an intrinsic parameter for failure initiation in bulk polymers.

Crack prediction for a partially solidified lead-free bronze casting using thermal stress analysis

For crack prediction in permanent mold casting of lead-free bronze, elasto-viscoplastic and elasto-plastic thermal stress analyses were performed and compared with the casting tests. The elastoviscoplastic model was constructed by the method which enables to determine rheological properties without steady state stress in experiments. Maximum deviatoric principal (only by the elastoviscoplastic analysis) and hydrostatic stress were in reasonable agreement with the locations of cold cracking and hot tearing in the casting tests, respectively. It was suggested that considering the rheological properties of semi-solid alloys was important especially to predict cracks during and after solidification

On the effect of hydrostatic stress on fatigue crack propagation

PurposeThe purpose of this paper is to study mutual interaction between von Mises equivalent and hydrostatic stresses at the crack tip area of an elastoplastic material in order to obtain critical conditions for crack propagation under fatigue loading.Design/methodology/approachA5083-H111 aluminum alloy is used to obtain a Chaboche-type constitutive equation, which is introduced in a commercial finite elements package to evaluate stress distribution at crack tip area. A simplified three-dimensional (generalized plane strain) grid is used, resulting in fast and accurate results. Numerical simulations are performed to connect crack propagation rate with various combinations of fatigue stress amplitude, initial crack length and number of loading cycles. Distance between characteristic points of stresses distribution in the crack tip area are compared to experimental fatigue crack growth rates in order to assess the validity of the present approach.FindingsIt is found that saturation of plastic strains, i.e. maximization of von Mises equivalent stress, is a prerequisite for hydrostatic stress to take a critical-maximum value, outside the plastically saturated zone. At the point of maximum hydrostatic stress brittle fracture is initiated, driving to separation of the ligament up to crack tip, without formation of new plastic strains. The length of this ligament is defined as crack propagation step, showing good agreement with experimental data.Originality/valueThe present approach seems to constitute a reasonable and adequate method for the description of fatigue crack propagation in terms of continuum mechanics, not necessitating microscopic considerations or empirical criteria lacking theoretical or physical basis. In addition, it liberates from the notion of stress intensity factors, strongly disputed beyond linear elasticity. Improved constitutive equations and numerical models are expected to drive in a complete fatigue failure criterion similar to those of static loading.

Multi-axial Fatigue Criteria with Length Scale and Gradient Effects

The objective of the work is first to extend some classic high cycle fatigue (HCF) criteria (as Crossland, Dang Van, Papadopoulos, ...) to take into account a sensitivity of the criteria to stress spatial variations occurring at length scale lg, and second to compare the performances of the extensions through numerical simulations of experimental fatigue tests. After an introduction of the basic criteria and their gradient based extensions proposed by Luu et al., we focus on the Crossland criterion to propose a more practical and simple expression taking into account the gradient of the stress amplitude and the maximum hydrostatic stress. The proposition is then tested and applied to different simple situations: 4-point bending and cantilever rotative bending. The relative errors between the exact solutions and the numerical simulations are estimated. Biaxial bending-torsion tests are also simulated to demonstrate the capabilities of the approach. The generalization of the approach to other multiaxial fatigue criteria is briefly shown through the case of Papadopoulos 2001 proposal. Finally, the present study develops a simple formulation of gradient multi-axial fatigue criteria extending the classical HCF criteria. In this work only stress gradient with a beneficial effect on fatigue have been considered.

The Effects of Non-Metallic Inclusion on Ductile Damage of High Carbon Steel Wire in Multi-Pass Dry Drawing Process

The objective of this study is to evaluate how the inclusion sizes influence the damage value and the maximum hydrostatic stress during multi-pass dry drawing process. It was well known that non-metallic inclusions can lead to material fracture during metal forming process, and be harmful to the quality of the final product. In multi-pass dry wire drawing, the temperature rise during deformation greatly decreases the quality of final product. In this study, the pass schedule in which initial diameter of 3.55 mm is reduced to final diameter of 2.115 mm was isothermally designed for the high carbon content steel. Spherical non-metallic inclusion of Al2O3 is located in the center of a steel rod. Influences of inclusion size, 5 μm, 10 μm, 20 μm and 50 μm in initial diameter 3.55 mm on ductile damage was investigated by FE-simulation in which material fracture was estimated using normalized Cockcroft and Latham criterion.