Evolution Of Stress Distribution Research Articles

Oligo-cyclic loading-induced evolution of stress distribution and apparent amorphous modulus in lamellar stacks of high-density polyethylene

Assessing the resistance of high-density polyethylene (HDPE) against earthquake-like loads involves understanding the changes in structure and properties induced by oligo-cyclic loading at various length scales. To study the evolution of stress distribution and intrinsic properties within lamellar stacks from pristine to oligo-cyclic loading pre-conditioned materials, simultaneous in-situ SAXS/WAXS measurements were performed. During the elastic deformation of each pristine and preconditioned sample, crystal strain was tracked using the in-situ WAXS technique. Based on the established elastic tensor of the crystalline structure in polyethylene, we calculated the microscopic stress values within crystalline lamellae. In the pristine sample, lamellar stacks exhibit closely series-like coupling in the equatorial region and parallel-like coupling in the polar region of the spherulite. In the pre-conditioned sample, stress is primarily concentrated in the intra-fibrillar region, where the crystalline and amorphous phases are series-coupled, and strong strain concentration occurs in the inter-fibrillar region. By combining the local strain in the amorphous layer within the lamellar stacks in the equatorial region of the spherulite and the intra-fibrillar region with series-coupled lamellar stacks, measured by in-situ SAXS tests, the apparent amorphous modulus at the lamellar stack scale can be determined. This modulus changes from 71 to 106 MPa in the equatorial region of pristine spherulites to a notable 2000–7000 MPa in the intra-fibrillar region under the influence of oligo-cyclic pre-loading. Importantly, this apparent modulus is affected by both crystallization conditions and molecular structure, with molecular parameters exerting the primary influence.

Numerical modeling considering initial gradient mechanical properties and experiment verification of residual stress distribution evolution of 12Cr2Ni4A steel generated by ultrasonic surface rolling

Ultrasonic surface rolling process is a promising surface strengthening technique which can improve the fatigue performance of metallic components by introducing reasonably compressive residual stress field. It is of great significance to accurately predict the residual stress distribution of parts in the simulation of ultrasonic surface rolling process. In this paper, a numerical model considering initial gradient mechanical properties (residual stress and micro-hardness) is proposed to predict the residual stress distribution of 12Cr2Ni4A carburized and quenched steel. Moreover, a method is proposed to calculate the ultrasonic surface rolling coverage based on Hertz contact theory, which can guide the optimization of process parameters. The effects of static load, rolling tool radius, amplitude and feed rate on residual stress distribution are investigated. The simulated results and measured results are compared and proved to be in good agreement, which validates the accuracy of the model proposed in this paper.

Numerical modeling and experimental verification of residual stress distribution evolution of 12Cr2Ni4A steel generated by shot peening

Shot peening is a widely used surface strengthening technique which can improve the fatigue life of metal components by introducing reasonably distributed compressive residual stress. The accurate prediction of residual stress distribution of parts is a tough challenge in the simulation of shot peening. In this paper, the numerical calculation of the residual stress of shot peening is investigated with 12Cr2Ni4A steel as the target. A two-dimensional Gaussian distribution model is proposed to calculate the number of impact shots. A method is proposed to calculate shot peening coverage using displacement and displacement gradient, which increases the identification accuracy of peened surface topography and provides a scientific method for coverage calculation. A random multi-shot finite element model for high strength steel is established considering the elastoplastic of shot. The effects of the process parameters, initial surface morphology and initial residual stress on the residual stress distribution after shot peening are investigated. The accuracy of the proposed method is verified by comparing the measured and simulated results. • A two-dimensional Gaussian distribution model is proposed to calculate the number of impact shots. • An improved model for predicting the residual stress distribution in shot peening is developed. • A method to calculate the shot peening coverage using displacement and displacement gradient is proposed. • The effects of treatment parameters and initial state on residual stress are studied. • The experiment is used to verify the proposed model.

Modeling the Spatial and Temporal Evolution of Stress during Multiworking Face Mining in Close Distance Coal Seams

Mining in close distance coal seams (CDCSs) is frequently associated with engineering disasters because of the complicated nature of stress distribution within CDCSs. In order to establish a layout of a roadway to minimize the occurrence of disasters associated with mining CDCS, here the spatial and temporal evolution of stress distribution during the multiworking face mining of a CDCS was explored through numerical simulation based on the engineering and geological conditions of the Nantun Coal Mine. The numerical simulation results indicate that, after the extraction of adjacent multiple working faces, the spatial distribution of stress can be characterized with areas of increased, reduced, and intact stress. The superposed stress of inclined seams that are very close to each other propagates through coal pillars in the bottom floor, and this propagation follows neither the line along the axis of the coal pillar nor the line perpendicular to the direction of the floor. It instead propagates along a line angled with the axis of the coal pillar. The roadway can be arranged in the area with reduced stress, to improve its the stability. Based on the computed spatial and temporal evolution of stress, an optimized layout of roadway was proposed. This layout features a reasonable interval between the mining roadway and a minimal proportion of increased stress areas along the mining roadway and is aligned with geological structures.

The Thermo-Mechanical Coupling Effect in Selective Laser Melting of Aluminum Alloy Powder.

In the selective laser melting process, metal powder melted by the laser heat source generates large instantaneous energy, resulting in transient high temperature and complex stress distribution. Different temperature gradients and anisotropy finally determine the microstructure after melting and affect the build quality and mechanical properties as a result. It is important to monitor and investigate the temperature and stress distribution evolution. Due to the difficulties in online monitoring, finite element methods (FEM) are used to simulate and predict the building process in real time. In this paper, a thermo-mechanical coupled FEM model is developed to predict the thermal behaviors of the melt pool by using Gaussian moving heat source. The model could simulate the shapes of the melt pool, distributions of temperature and stress under different process parameters through FEM. The influences of scanning speed, laser power, and spot diameter on the distribution of the melt pool temperature and stress are investigated in the SLM process of Al6063, which is widely applied in aerospace, transportation, construction and other fields due to its good corrosion resistance, sufficient strength and excellent process performance. Based on transient analysis, the relationships are identified among these process parameters and the melt pool morphology, distribution of temperature and thermal stress. It is shown that the maximum temperature at the center point of the scanning tracks will gradually increase with the increment of laser power under the effect of thermal accumulation and heat conduction, as the preceded scanning will preheat the subsequent scanning tracks. It is recommended that the parameters with optimized laser power (P = 175–200 W), scanning speed (v = 200–300 mm/s) and spot diameter (D = 0.1–0.15 mm) of aluminum alloy powder can produce a high building quality of the SLM parts under the pre-set conditions.

Fatigue Crack Growth in Plastically Compressible Solids: Role of Negative Stress Ratio, Plastic Compressibility and Strain Softening

The effect of cyclic loading on fatigue crack growth in plastically compressible solids is investigated at negative stress ratio under plane strain and small scale yielding conditions. The material is characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The plastic crack growth, crack tip opening displacement (CTOD) and near crack tip stress fields are presented using finite element method. Material hardening/ softening has a major relevance on crack growth, CTOD and the evolution of stress distribution. It is revealed here that the negative stress ratio can significantly influence the loading conditions at the crack tip and thereby increase the crack growth for tension–compression loading for hardening material whereas the fatigue crack growth of plastically compressible hardening-softening-hardening material is only slightly affected by the negative stress ratio albeit it is accepted in literature that compressive loads contribute to fatigue crack growth significantly. In the present studies, the CTOD variation with applied load and the near stress distribution are also very unusual in nature.

Experimental and theoretical study of mechanical properties of root-soil interface for slope protection

Plant roots mechanically enhance the strength of soil and improve slope stability through anchoring. Given the popularization of ecological slope-protection technology, a quantitative study of how roots help to anchor soil is highly pertinent. The object of the present study is thus to investigate how roots and soil combine to affect the mechanical properties of the root-soil interface. Toward this end, pullout experiments of cedar roots of different diameters in soils of different density were conducted. The experimental results show that the maximum pullout force increases significantly with increasing root diameter, but only slightly increases with increasing soil density, which indicates that the root diameter has a greater impact on the maximum pullout force than soil density. Next, based on studies of fiber-reinforced composites, a root-soil pull-out model was proposed to study the evolution of shear stress on root-soil interface. This approach ensures that the model accurately reflects the dynamic stress distribution evolution at the root-soil interface and can calculate the pullout process of embedded root from soil. The accuracy of the model is verified by comparing the calculated results with experimental results. Finally, how soil density and root diameter affect the anchoring force was analyzed. The results indicate that the maximum anchoring force increases linearly with increasing root diameter, but nonlinearly with increasing soil density until reaching a fixed value. These results show that the root soil pull-out model has significant practical value in slope protection.

Residual stress distribution in built-in beams

Metallic hyperstatic structures, like beams, submitted to excessive loads, do not fail completely before fully yielding in more than one cross section. Indeed, for built-in beams, three cross sections must be fully yielded before the final failure can occur. So, modeling the evolution of the cross-section residual stress distribution is an important subject that should be addressed to guarantee the stress analysis modeling correctness. This paper analyses the residual stress distribution evolution, in critical cross sections, of built-in beams during a transversal concentrated load growth, until the final failure through hinges formation. A finite element model is also presented. The results show good matches with the numerical model, used as a reference.

Stiffness-toughness balance in PP/EPDM/SiO2 ternary blend-nanocomposites: The role of microstructural evolution

The effect of microstructural evolution with hydrophilic-nanosilica (SiO2) concentration, ranging from 0 to 5 wt%, on mechanical properties and deformation micromechanisms of PP/EPDM/SiO2 (80/20/x) ternary blend-nanocomposites was investigated. Morphological observations revealed that, SiO2 nanoparticles tend to localize either around the dispersed EPDM particles or at the PP/EPDM interface, promoting the formation of three dimentional network-like EPDM/SiO2 composite structures dispersed in the PP matrix, especially at higher SiO2 loadings. This type of dispersion state was further confirmed by the rheological analysis. Synergistic toughening effect of soft EPDM particles and rigid SiO2 particles under Izod impact test was observed in these ternary systems, so that the materials with a better balance of stiffness/toughness were achieved. The results demonstrated that the extent of impact toughness increase is higher, where a large amount of the SiO2 nanoparticles surrounded the EPDM dispersed particles distributed in the PP matrix. This significant increase was attributed to the change in the size of stress concentration region and evolution of stress distribution throughout the material. The failure mechanisms were studied, and the underlying toughening micromechanisms were proposed.

Assessment of the Time-dependent Behaviour of a Reinforced Concrete Water Tank by using the Finite Elements Method

Determinants factors (design and execution errors, site location, environmental & exploitation conditions) could generate the over-time degradation of the buildings. In order to assure the safety during the service period (imposed by the norms) the time-dependent monitoring of the structure’s behaviour is required. As a case study a reinforced concrete water tank was analysed. The structural analysis in two different stages was considered: initial stage (as in design project) and current stage (after approximately 35 years of exploitation). A parametric study based on a computational model (by using Finite Element Method - FEM) was carried out using SCIA Engineer software program. The computational model was designed (for both stages) by using mechanical characteristics of the material (collected from initial project) and data resulted from destructive and non-destructive tests in current stage. The objective was to estimate the level of degradations which could occur in structural elements during the exploitation period by comparing the evolution of stress distribution in the two stages. The durability factors were analysed in order to the studied structure’s life-cycle assessment.

Simulation of fire resistance behaviour of pultruded GFRP beams – Part II: Stress analysis and failure criteria

This two-part paper presents a numerical study on the fire resistance behaviour of pultruded GFRP profiles with square tubular cross-section simultaneously subjected to four-point bending and the standard fire of ISO 834. The first part [1] presented the numerical models and results focused on the most relevant kinematic issues (deflections and strains), while this second part (present paper) reports numerical results associated to the static issues, particularly the evolution of stress distributions and failure initiation with fire exposure time. The paper first presents and discusses the evolution of stress distributions in both longitudinal and transversal directions of an unprotected GFRP beam under one-side fire exposure (reference beam). Next, the influence of using a fire protection system and exposing the beams to fire in three sides is assessed by comparison with the case of reference beam. Additionally, the Tsai-Hill failure (initiation) criterion was used to identify the zones (sections and points) of GFRP beams that are most sensitive to failure due to high temperatures. The numerical results obtained show that (i) longitudinal stresses across the section become highly nonlinear as a result of temperature increase; (ii) shear stress diagram is severely affected by fire exposure in three sides; (iii) transversal stresses are negligible compared to the longitudinal and shear ones; and (iv) the collapse of beams (considering Tsai-Hill failure analysis) occurs due to top flange and web (top part) failure, which generally agrees with experimental observations.

Simulation of fire resistance behaviour of pultruded GFRP beams – Part I: Models description and kinematic issues

This two-part paper presents a numerical study about the fire resistance behaviour of pultruded GFRP profiles with square tubular cross-section subjected to bending and the ISO 834 time-temperature curve. The first paper deals with the development of numerical and analytical models and the discussion of relevant kinematic issues, including the evolution of beam deflection and position of neutral axis with the fire exposure time. The second part [1] reports an in-depth investigation on the side of static issues, which include the evolution of stress distributions and failure initiation with the fire exposure time. In the present paper, three–dimensional finite element models were developed to simulate fire resistance tests previously conducted by the authors on GFRP beams, in which different degradation curves were considered for compressive, tensile and shear moduli, based on experimental data. In these numerical simulations, both effects of varying the assignment of material properties (depending on the position of neutral axis) and of considering different thermal expansion coefficients were taken into account, and some conclusions were drawn on their influence on mid-span deflection evolutions. Since no failure criterion was implemented, both models were not able to reproduce the failure of the beams, but the overall tendency of the numerical results was consistent with the experimental data. Alongside the numerical study, analytical models based on Timoshenko beam theory were also developed and allowed obtaining accurate predictions of the mid-span deflection evolution of the GFRP beams; the analytical results were in close agreement with the numerical ones and also with the experimental data.

Effect of Thermal Mechanical Behaviors of Cu on Stress Distribution in Cu-Filled Through-Silicon Vias Under Heat Treatment

Through-silicon vias (TSV) are facing unexpected thermo-mechanical reliability problems due to the coefficient of thermal expansion (CTE) mismatch between various materials in TSVs. During applications, thermal stresses induced by CTE mismatch will have a negative impact on other devices connecting with TSVs, even leading to failure. Therefore, it is essential to investigate the stress distribution evolution in the TSV structure under thermal loads. In this report, TSVs were heated to 450°C at different heating rates, then cooled down to room temperature after a 30-min dwelling. After heating treatment, TSV samples exhibited different Cu deformation behaviors, including Cu intrusion and protrusion. Based on the different Cu deformation behaviors, stress in Si around Cu vias of these samples was measured and analyzed. Results analyzed by Raman spectrums showed that the stress distribution changes were associated with Cu deformation behaviors. In the area near the Cu via, Cu protrusion behavior might aggravate the stress in Si obtained from the Raman measurement, while Cu intrusion might alleviate the stress. The possible reason was that in this area, the compressive stress $$ \sigma_{\theta }$$ induced by thermal loads might be the dominant stress. In the area far from the Cu via, thermal loads tended to result in a tensile stress state in Si.

Cavitation analysis of spherical shock wave evolution in concrete medium

This paper investigates the dynamic spherical cavity expansion of shock wave evolution in concrete medium described by compressible Drucker–Prager plasticity with locked hydrostat. Hugoniot jumping conditions across shock waves are fully accounted for and a complete description of the motion and stress distribution evolution is obtained for different response domains. By solving the dimensionless governing differential equations during different periods, numerical illustrations are then developed with application to an explosion scenario inside an infinite concrete medium. The parameter study indicates that the equivalent charge weight of TNT proportionally affects the shock waves evolution, while the standoff distance has an inversely proportional impact on the ultimate locked/compacted boundary area.

Model for Stress Generation and Flow in Anodic Oxides

Porous anodic oxide (PAO) films are grown by electrochemical polarization of Al, Ti, and other metals in baths that dissolve the oxide. Procedures to grow films with highly ordered and controllable arrangements of nanoscale pores have led to the extensive use of PAO films in nanofunctional devices. Experiments and calculations show that transport in the oxide occurs by electrical migration coupled with oxide flow driven by mechanical stress (1-3). Pores initiate by a morphological instability at the oxide-solution interface when the initially formed barrier oxide reaches a critical thickness (4). In another presentation at this meeting, we showed that this instability is preceded by the buildup of compressive stress due to localized electric field-induced electrolyte anion incorporation at the oxide-solution interface. The instability is modeled by competition between stabilizing oxide formation at the oxide-solution interface and destabilizing oxide flow driven by gradients of anion-induced surface stress. The model predicts important features of self-ordered PAO growth on many metals: the pore separation-voltage scaling ratio, the narrow ranges of anodizing efficiency, and the threshold electric field. Characteristics of anodic oxides that enable self-organized PAO formation include their ability to flow and to accumulate highly localized stress at interfaces due to electrochemical reactions. Here we report a new model for coupled interfacial reactions, electrochemical transport and mechanics of amorphous anodic oxides. In the model, ionic conduction occurs by high-field electrical migration of oxygen and metal vacancy type defects. In contrast with other point defect models, vacancies are created and destroyed homogeneously within the oxide by electric-field stimulated localized relaxations of the amorphous network. Vacancy creation expands the oxide network generating compressive stress, while vacancy destruction contracts the network producing tensile stress. Field-stimulated vacancy formation and removal affect the conductance of anodic films and hence may be probed by electrochemical impedance spectroscopy (EIS). Impedance measurements during steady-state Al anodizing in sulfuric and oxalic acids are presented. The spectra reveal inductive loops between 1 and 100 Hz as reported elsewhere (5). The characteristic time constant and resistance of the inductive loop are shown to be determined by the kinetic parameters of the vacancy formation/removal reaction. The values of these parameters are independent of anodizing current density or solution composition. The kinetic model for vacancy formation/removal identified by EIS was used to simulate evolution of stress distributions in the oxide during Al anodizing in phosphoric acid at a constant current density of 5 mA/cm2 (6). Calculations demonstrate that vacancies are continuously generated at the oxide-solution interface to accommodate incorporation of large electrolyte oxyanions. This process is shown to be quantitatively consistent with localized compressive stress buildup at this interface as revealed by in situ stress measurements, the precursor for oxide flow and pore formation. At the metal interface, vacancies produced by metal oxidation are destroyed continuously at the metal interface, consistent with the buildup of localized tensile stress found experimentally. Finally we discuss implications of vacancy formation/removal for oxide flow. It is argued that at sufficiently high stress levels, this reaction can account for displacement of oxide volume driven by stress gradients. Such a process is equivalent to vacancy creep and can explain the apparent viscous flow of anodic oxides reported in several papers (1-3,7). ACKNOWLEDGMENT This work was supported by the the National Science Foundation through NSF-CMMI-100748. REFERENCES 1. S. J. Garcia-Vergara et al., Electrochim. Acta. 52, 681 (2006). 2. J. E. Houser and K. R. Hebert, Nature Mater. 8, 415 (2009). 3. J. Oh and C. V. Thompson, Electrochim. Acta, 56, 4044 (2011). 4. K. R. Hebert et al., Nature Mater. 11, 162 (2012). 5. M. Curioni et al., Electrochim. Acta 55, 7044 (2010). 6. Ö. Ö. Çapraz, et al., Electrochim. Acta 167, 404 (2015). 7. D. H. Bradhurst and J. S. L. Leach, J. Electrochem. Soc., 113, 1245 (1966).

Complex events in a fault model with interacting asperities

The dynamics of a fault with heterogeneous friction is studied by employing a discrete fault model with two asperities of different strengths. The average values of stress, friction and slip on each asperity are considered and the state of the fault is described by the slip deficits of the asperities as functions of time. The fault has three different slipping modes, corresponding to the asperities slipping one at a time or simultaneously. Any seismic event produced by the fault is a sequence of n slipping modes. According to initial conditions, seismic events can be different sequences of slipping modes, implying different moment rates and seismic moments. Each event can be represented geometrically in the state space by an orbit that is the union of n damped Lissajous curves. We focus our interest on events that are sequences of two or more slipping modes: they show a complex stress interchange between the asperities and a complex temporal pattern of slip rate. The initial stress distribution producing these events is not uniform on the fault. We calculate the stress drop, the moment rate and the frequency spectrum of the events, showing how these quantities depend on initial conditions. These events have the greatest seismic moments that can be produced by fault slip. As an example, we model the moment rate of the 1992 Landers, California, earthquake that can be described as the consecutive failure of two asperities, one of which has a double strength than the other, and evaluate the evolution of stress distribution on the fault during the event.

Prediction of matrix-to-cell stress transfer in heart valve tissues.

Non-linear and anisotropic heart valve leaflet tissue mechanics manifest principally from the stratification, orientation, and inhomogeneity of their collagenous microstructures. Disturbance of the native collagen fiber network has clear consequences for valve and leaflet tissue mechanics and presumably, by virtue of their intimate embedment, on the valvular interstitial cell stress-strain state and concomitant phenotype. In the current study, a set of virtual biaxial stretch experiments were conducted on porcine pulmonary valve leaflet tissue photomicrographs via an image-based finite element approach. Stress distribution evolution during diastolic valve closure was predicted at both the tissue and cellular levels. Orthotropic material properties consistent with distinct stages of diastolic loading were applied. Virtual experiments predicted tissue- and cellular-level stress fields, providing insight into how matrix-to-cell stress transfer may be influenced by the inhomogeneous collagen fiber architecture, tissue anisotropic material properties, and the cellular distribution within the leaflet tissue. To the best of the authors' knowledge, this is the first study reporting on the evolution of stress fields at both the tissue and cellular levels in valvular tissue and thus contributes toward refining our collective understanding of valvular tissue micromechanics while providing a computational tool enabling the further study of valvular cell-matrix interactions.

Numerical study of the interaction between adjacent galleries in a high-level radioactive waste repository

In the framework of the feasibility study of high-level radioactive waste geological disposal, the potential interaction between adjacent galleries is an important issue to the layout design of the repository. Based on some experimental investigations by ANDRA, the present work is devoted to provide a preliminary evaluation on this phenomenon by a series of numerical simulations. According to the repository concept in France, the multi-barriers system, composed of geological and engineered barriers, is adopted for the construction of underground repository. The engineered barriers mainly include the canister, the concrete and the clay embankment. In the study, the hydromechancial behaviour of host rock (claystone) and concrete are characterized by a coupled elastoplastic damage model. On long-term scale, the creep of host rock as well as the chemical degradation of concrete is taken into account. A nonlinear elastic model of the classical Cam-clay type is applied to the bentonite plug. The numerical simulations are then performed for adjacent galleries with different inter distances. The evolution of stress distribution, pore pressure, and inelastic zone are analysed which can help the engineers to get a good understanding on the interaction of adjacent galleries. Finally, based on the predictive results, the minimum interdistance between galleries is discussed.

Numerical study on the evolution of stress distribution in cellular microstructures

Abstract Stress generation and evolution in a cellular microstructure observed in the directional solidification process of a binary alloy system were simulated using a phase field model. The Ni–Cu system was chosen as a typical alloy, and two-dimensional simulations were carried out. The elastic stress induced by the volumetric contraction due to solidification was considered, and stress distribution in the solidified region was calculated. Results showed that a complex stress state is generated in the interfacial region, while it is homogeneous in the bulk solid. Under a condition causing the growing cells to coalesce, remarkably large stress was observed at the tip of the decayed cell, leading to a stress concentration around the liquid droplets and grooves subsequently generated. In order to show the effect of binary composition on the stress distribution, the dependence of Cu concentration on the elastic coefficient was considered, and simulations were carried out. Consequently, stress distribution in the bulk solid was observed along the cell boundaries, while no stress distribution was generated when this dependence was not taken into consideration.

Stress distribution evolution in a ceramic body during firing. Part 2. Profile calculation

Stress distribution during firing is reported. The calculation is performed based on the model stated in the part 1. Starting data correspond to the constitutive models presented in part 1. Besides, an experimental measurement was performed to obtain the Young modulus and the thermal dilatation to be considered for calculations. Starting from the stress equilibrium, it may be reported that: 1) The stress distribution during hot forging is always similar in spite of different pressing conditions and different considered constitutive behaviors. 2) The thermo-elastic behavior may be considered as an acceptable approximation. 3) The temperature gradients and their effect on the body viscosity and on thermal dilatation play an essential role in the stress distribution.