Minimum Strain Energy Research Articles

Application of modified fracture criteria incorporating T-stress for various cracked specimens under mixed mode I-II loading

Accurate assessment of fracture behavior and life prediction of cracked materials based on the mixed mode fracture criteria is of utmost importance in fracture mechanics. In this study, the modified fracture criteria incorporating T-stress for mixed mode I-II cracks were comprehensively reviewed. Additionally, a comparative analysis was conducted between the experimental results obtained from five different cracked configurations and the theoretical predictions according to these modified criteria. Moreover, a brief discussion was held regarding the effect of T-stress on both crack initiation angle and fracture toughness, accompanied by providing some suggestions. The results revealed that the predictive accuracy of modified criteria exhibited noticeable variations across different cracked configurations due to the significant disparities in both the sign and magnitude of T-stress around the crack tip. However, it was observed that the predicted curves based on the modified fracture criteria for the semi-circular bend and edge-crack triangular specimens had remarkable similarities owing to their similar biaxial stress ratio B. When the mode II loading dominated, the generalized maximum tangential stress, generalized minimum strain energy density and generalized averaged strain energy density criteria were suitable for the semi-circular bend, edge-crack triangular, central crack rectangular and short bend beam specimens with positive T-stresses, whereas the maximum tangential strain, generalized maximum tangential stress and generalized maximum tangential strain energy density criteria could provide better theoretical predictions for central cracked Brazilian disk specimens having a negative T-stress.

Railway transition zones: evaluation of existing transition structures and a newly proposed transition structure

ABSTRACT This comprehensive study addresses the persistent issue of railway transition zone degradation, evaluating the efficacy of the most commonly used mitigation measures and proposing a novel Safe Hull-Inspired Energy Limiting Design (SHIELD) of a transition structure. Firstly, this work assesses the traditional transition structures, including horizontal and inclined approach slabs and transition wedges, using commonly studied responses (kinematic response and stress) and a recently proposed criterion based on total strain energy minimization. The second part of the paper evaluates the newly introduced transition structuress (SHIELD) using the same criterion as used for the evaluation of the traditional transition structures. A detailed investigation of existing and a new design using a 2-dimensional finite element model shows SHIELD’s effectiveness in managing energy flow at transition zones and provides reasoning behind the ineffectiveness of the other commonly used transition structures. The study demonstrates the robustness and comprehensiveness of the recently developed energy-based criterion and its applicability to different types of transition zones. Moreover, it highlights the potential of SHIELD as a solution to address the complexities associated with the design of railway transition zones.

Achieving atomically flat copper surface: Formation of mono-atomic steps and associated strain energy mechanisms

Recent studies have demonstrated that achieving an atomically flat surface for metals can significantly enhance their oxidation resistance and further advance their electronic-optical applications. However, traditional heat treatments for polycrystalline metals tend to create numerous low-surface-energy steps and facets due to surface energy minimization. Moreover, surface diffusion is further limited by three-dimensional Ehrlich-Schwoebel barriers due to the formation of steps and facets. Therefore, achieving atomically flat surfaces is energetically unfavorable and kinetically unstable. Here, we covered graphene (Gr) on Copper (Cu) surface and performed systematic and statistical analysis of microstructures on three types of graphene-Cu (Gr/Cu) interfaces: annealed Cu, transferred and high-temperature deposited Gr/Cu interfaces. We found that mono-atomic steps formed at high-temperature deposited Gr/Cu interface, in comparison with multi-atomic steps at annealed Cu and transferred Gr/Cu interfaces. Molecular statics/dynamics simulations and thermodynamic analysis suggest that formation of mono-atomic steps can be ascribed to the minimization of Gr strain energy and high-temperature assisted surface diffusion. When a step height (h) is smaller than five atomic planes (h < 5), strain energy minimization of Gr will prevent step bunching (a non-uniform surface morphology), accelerate the formation of atomically flat surface. When h ≥ 5, Gr strain energy minimization will trigger step-bunching instability, decompose large steps and thus facilitate the surface diffusion to develop atomically flat surface. The present results may suggest a potential strategy to achieve atomically flat surface of bulk metals by high-temperature treatment.

Design of partially covered bilayer thin film actuators

One approach to create bending deformation using active materials is to fully cover a passive substrate with the active material. The active layer expands/contracts in response to an external stimuli, while, the passive layer does not deform, thereby, generating a strain gradient through the thickness, and hence, bending. However, a recent experimental study [Pozo, M et al. ACS Appl. Mater. Interfaces, 13, 59381–59391 (2021).] showed that a partially covered (40%) bilayer deformed as much as the “standard” fully covered bilayer. To elucidate such a non-standard response of bilayers, we have developed an analytical model using the strain energy minimization. The developed model showed that the deformation of the bilayer may actually either increase or decrease or saturate with the increase in the coverage depending on the moduli ratio and the thickness ratio of the active and passive layers. Design strategies for actuators considering their curvature and bending stiffness are proposed based on the implications of the developed model. The present study also shows the potential for designing patterned actuators with multiple coverings (may have multiple active layers that are responsive to different stimuli) to realize different actuations based on the choice of the trigger from a single actuator creating multi-modal, multi-stimuli-responsive actuators.

Modeling, testing, and optimization of novel lattice structures for enhanced mechanical performance

Cellular materials have drawn increasing interest in numerous applications due to their promising specific stiffness, strength and energy absorption capacity. In this work, a variety of rather novel lattice topologies pertinent to additive manufacturing are derived and examined. A number of these are derived by free-domain and constrained domain topology optimization procedures, while others are inspired by the triply periodic minimum surface (TPMS) sheet-based topologies. The topology optimization module utilized a single objective function of minimizing strain energy under linear elastic conditions. A total of fifteen different lattice topologies are investigated numerically, including both novel and conventional topologies (e.g. strut-based lattices) and their effective elastic properties are determined with respect to relative density through finite element analysis (FEA). Based on the preliminary FEA results, a number of these topologies are selected of which tessellated lattice structures are fabricated through laser powder bed fusion (LPBF) additive manufacturing technique out of Nylon thermoplastic material. The tessellated lattice structures are experimentally tested in compression and their mechanical performance, including uniaxial modulus, yield strength, and energy absorption capacity (EAC), is assessed. FEA simulations have been conducted using an elastic-plastic constitutive model for the Nylon base material. Both the experimental and numerical results reveal that the mechanical performance of the novel tube-based TPMS lattice P-100 and the combined loading (CL) topology derived through free-domain topology optimization surpasses all other topologies. P-100 uses a primitive TPMS with equal-length tubular connections in each direction, where the tubular length percentage compared to the primitive lattice size is 100%, while CL lattice topology is a free domain topology optimized under compressive loads on the centers of faces, edges, and vertices toward the center. The innovative lattice topologies proposed in the current study, particularly the P-100 and CL topologies, can become crucial in applications where it is necessary to improve the energy absorption capacity, such as sandwich panel cores, supports, and infills for 3D printed components.

A new criterion based on the ratio of strain energy density for mixed-mode crack initiation prediction in ductile materials

In consideration of the different mechanisms of microscopic separation governed by dilation and microscopic shearing controlled by distortion on crack initiation, a new criterion based on the ratio of two strain energy densities (RSED) is proposed by differentiating the dilatational and distortional parts in strain energy density. The influence of the weights of two strain energy densities under different stress states on fracture resistance of crack initiation is also considered in the RSED criterion. The size and shape of the core region do not affect the direction and fracture resistance of crack initiation predicted by the RSED criterion. Moreover, the direction predicted by the RSED criterion is theoretically demonstrated to be identical to the orientations predicted by the maximum stress triaxiality (MST) criterion and the T criterion on crack initiation. The crack initiation directions which are obtained by the experiments for different materials and predicted by various criteria are found to be mostly coincident near the mode-I crack, and so are the fracture resistances. In the vicinity of the mode-II crack, the direction of crack initiation predicted by the RSED criterion shows a superior consistency for the experimental results of the ductile materials reported by Theocaris et al. (1982) and Kong et al. (1995) over the three classical criteria, such as the maximum tangential stress (MTS), the maximum energy release rate (MERR) and minimum strain energy density (MSED). The RSED criterion also has the potential to amend the issue of the underestimation for KIIC/KIC in some typical materials, e.g., the face-centered-cubic (f.c.c) metals. Therefore, the RSED criterion prefers to predict the direction and fracture resistance of crack initiation in ductile materials.

Design optimization of soft robotic fingers biologically inspired by the fin ray effect with intrinsic force sensing

Soft grippers display adaptability, dexterity, and safety, garnering increased interest in their applications. However, accurately modeling their nonlinear deformation and sensing the grasping force remain challenging. Here, a generalized closed-form kinetostatic model of a biomimetic FRE soft finger is established based on the chained-beam-constraint model. A methodology combining a geometry-based contact constraint technique is presented, utilizing the minimum strain energy principle for sensorless, precise, and rapid estimation of the deformed contours and contact force when the FRE finger grasps an arbitrary object with a continuous surface. Method verification using FEA demonstrates a maximum error of no more than 1.28% and 2.44% for the contour and contact force estimation, respectively. Subsequently, a multiobjective genetic algorithm is used to optimize the FRE finger design for better adaptability and greater grasping force in a special scenario. Finally, the finger's capability to accurately perceive grasping force and deformed contours was demonstrated by four groups of grasping tests using cylinder and cube objects, with maximum average absolute error and relative error of 0.083 N, 9.84%, and 1.335 mm, 10.06%, respectively.

Lightweight design of automotive front rail based on topology optimisation and collision analysis

On the premise of meeting the crash performance, in order to reduce the weight of the front rail of the automotive and improve the level of lightweight of the vehicle.Combining with the goal of ‘carbon reduction‘, a method of topology optimisation was used to optimise the lightweight performance of automotive front rail.Topology optimisation takes the front rail of the automobile as the research object, the installation area of the front rail as the design space of topology optimisation, the minimum strain energy as the optimisation goal, the relative density of the grid of each element as the design variable, and the mass fraction of the front rail as a constraint to design the topology optimisation. Then the optimal material distribution of the front rail of the vehicle is obtained. On this basis, the geometric dimensions of the section of the front rail are multi-objective optimised, the sample data are designed and the response surface model of optimisation objective are established through the design of the Latin square experiment. Based on the NSGA-II algorithm, the optimised mathematical model is solved by multi-objective optimisation. The results show that the weight of the optimised structure is reduced by 6.5% compared with the original structure, and the collision absorption energy is improved, and the peak acceleration is significantly reduced.

High-throughput first-principles investigation on grain boundary segregation of alloying elements in ferritic steel

By employing high-throughput first-principles calculations, the segregation capacity of fifteen widely used metallic alloying elements (viz., Be, Mn, Co, Cr, Ni, Al, Mo, W, Mg, Ta, Nb, Sb, Sn, Zr, and Bi) at ∑3 grain boundary in low alloy ferritic steel, as well as their impact on grain boundary stability, interfacial separation work, and other properties, were systematically investigated. The findings reveal that, for alloying atoms Sb, Sn, Bi, Nb, and Zr, whose size is notably larger than that of the matrix Fe atoms, the effect of strain energy minimization in segregation is comparable to that of chemical energy minimization. Furthermore, the impact of strain energy minimization is closely related to the volume of the alloying atoms both at the solid solution sites in the crystal and at the segregation sites at the grain boundary. Thus, the segregation of large alloy atoms on the grain boundaries can be predicted by atomic volume of each segregation site, which can provide valuable insights for the development of new alloys and for grain boundary engineering.

Topology Optimization of Wing Ribs for Additive Manufacturing

This paper describes the design of a lightweight wing rib structure by combining topology optimisation with additive manufacturing. In addition, a deep feed-forward neural network model is proposed to perform the load prediction for the constructed wing structure incorporated with this optimised rib. The strain energy of the front rib has a minimum strain energy 1330 J for the initial volume state when the topology is not optimised for lightweighting. The relative error of the load prediction values obtained by the output layer of the deep feed-forward neural network is less than 0.02%. The absolute error of the small load prediction was less than 0.30 N. The presented results demonstrate the viability of additive manufactured rib and its implementation in global wing load prediction model for faster designs.

Mixed mode crack growth behaviour considering plasticity-induced and roughness-induced closure

A theoretical analytical solution of the Christopher-James-Patterson (CJP) model in mixed mode is presented in this paper, where the influence of roughness-induced crack closure (RICC) on fatigue crack growth is considered and a new effective stress intensity factor range (ΔKP-R) is proposed as the driving force for crack propagation. The solution showed that both the maximum tangential stress criterion (MTS) and the minimum strain energy density criterion (S) can reasonably well predict the crack deflection angle. Experimental testing on EA4T axle steel samples showed that both the 8 % compliance offset criterion in the conventional ASTM procedure and the parabolic-line method were suitable for the determination of the crack-opening force. The solution includes plasticity-induced crack closure (PICC) and RICC effects, therefore the crack propagation behaviour can be described in a more effective way. Compared with the traditional mixed model crack growth models with higher fitting correlation coefficient, the fitting effect of the CJP model has been improved by 12 % in this solution, and the residual stress in the pre-crack stage increased the crack-closure level. Due to the influence of residual stress, the rate of roughness value (RA) showed a fluctuation of 4.5 %, which indirectly affected the fatigue crack growth rate (FCGR) of the test.

Multi-point incremental bending of doubly curved high strength steel sheet under minimum strain energy loading path

Multi-point incremental bending of doubly curved high strength steel sheet under minimum strain energy loading path

Interface Effects of Strain-Energy Potentials on Phase Transition Characteristics of VO2 Thin-Films.

Metal-insulator-transition (MIT) of VO2 has attracted strong attention as a potential phenomenon to be utilized in nanostructured devices. Dynamics of MIT phase transition determines the feasibility of VO2 material properties in various applications, for example, photonic components, sensors, MEMS actuators, and neuromorphic computing. However, conventional interface strain model predicts the MIT effect accurately for bulk, but fairly for the thin films, and thus, a new model is needed. It was found that the VO2 thin film-substrate interface plays a crucial role in determining transition dynamics properties. In VO2 thin films on different substrates, coexistence of insulator-state polymorph phases, dislocations, and a few unit cell reconstruction layer form an interface structure minimizing strain energy by the increase of structural complexity. As a consequence, MIT temperature and hysteresis of structure increased as the transition enthalpy of the interface increased. Thus, the process does not obey the conventional Clausius-Clapeyron law anymore. A new model is proposed for residual strain energy potentials by implementing a modified Cauchy strain. Experimental results confirm that the MIT effect in constrained VO2 thin films is induced through the Peierls mechanism. The developed model provides tools for strain engineering in the atomic scale for crystal potential distortion effects in nanotechnology, such as topological quantum devices.

Finite element method on topology optimization applied to laminate composite of fuselage structure

Abstract This research applies a numerical study of topology optimization of laminate composite structures by using a finite element method (FEM). In this methodology, the plies orientation is excluded from the optimization. The geometry-based optimization from frames of a MALE UAV fuselage structure is presented. The minimum strain energy with an optimization constraint of 20% of weight reduction is used in the objective function. Before the primary analysis, benchmark studies of topology optimization without considering orientations from previously published literature are performed. The convergence studies were taken to acquire the appropriate mesh size in the FEM technique, which utilized a four-noded shell element. The finite element analysis and optimization results showed that the structural design of the newly framed composite fuselage MALE UAV meets the structural strength requirements specified in the airworthiness standard STANAG 4671.

Hertzian crack propagation in graded glass/ceramic composites

AbstractIn literature, the concept of material gradation is shown to inhibit surface crack initiation in glass/ceramic composites subjected to Hertzian indentation. However, surface cracks could yet initiate due to relatively higher loadings or in the presence of surface flaws/defects. Hence, characterization of graded composites concerning the resistance against Hertzian crack initiation and propagation manifests itself as a prominent matter. In this study, axisymmetric Hertzian cracks evolving in graded glass/ceramic composites propelled by a rigid cylindrical punch are investigated employing a novel recursive method, called the stacked‐node propagation procedure. Crack trajectories and their propagation susceptibilities are predicted via the minimum strain energy density (MSED) criterion regarding the crack growth resistance (R‐curve) of ceramics. The stress trajectory approach is also considered for a homogeneous glass to reveal the reliance and effectiveness of the MSED criterion in the present crack problems. The Mori–Tanaka relations are adopted to model the elastic modulus and Poisson's ratio variations through the composites, which are implemented on the simulations via the homogeneous finite element approach. Hertzian crack problem of a practically producible graded composite comprised of oxynitride glass and a fine‐grained silicon nitride ceramics (Si3N4) is treated as a case study. The degree of material gradation is assessed for the mitigation of surface crack initiation and propagation risks.

Ion kinetic energy- and ion flux-dependent mechanical properties and thermal stability of (Ti,Al)N thin films

Ion-irradiation-induced changes in structure, elastic properties, and thermal stability of metastable c-(Ti,Al)N thin films synthesized by high-power pulsed magnetron sputtering (HPPMS) and cathodic arc deposition (CAD) are systematically investigated by experiments and density functional theory (DFT) simulations. While films deposited by HPPMS show a random orientation at ion kinetic energies (Ek)>105 eV, an evolution towards (111) orientation is observed in CAD films for Ek>144 eV. The measured ion energy flux at the growing film surface is 3.3 times larger for CAD compared to HPPMS. Hence, it is inferred that formation of the strong (111) texture in CAD films is caused by the ion flux- and ion energy-induced strain energy minimization in defective c-(Ti,Al)N. The ion energy-dependent elastic modulus can be rationalized by considering the ion energy- and orientation-dependent formation of point defects from DFT predictions: The balancing effects of bombardment-induced Frenkel defects formation and the concurrent evolution of compressive intrinsic stress result in the apparent independence of the elastic modulus from Ek for HPPMS films without preferential orientation. However, an ion energy-dependent elastic modulus reduction of ∼18% for the CAD films can be understood by considering the 34% higher Frenkel pair concentration formed at Ek=182 eV upon irradiation of the experimentally observed (111)-oriented (Ti,Al)N in comparison to the (200)-configuration at similar Ek. Moreover, the effect of Frenkel pair concentration on the thermal stability of metastable c-(Ti,Al)N is investigated by differential scanning calorimetry: Ion-irradiation-induced increase in Frenkel pairs concentration retards the wurtzite formation temperature by up to 206 °C.

Investigation of the strut‐and‐tie model of a single‐plane cable‐stayed bridge tower under vertical component of the cable force

AbstractThe design of reinforcement of concrete pylons in cable‐stayed bridges is a challenging task. Usually, only the influence of the strong horizontal component of the cable force is considered during the reinforcement design of the concrete tower, while the bursting forces caused by the vertical components of the cable forces are ignored. However, the latter is also an important factor for concrete cracking in bridge towers. In this paper, the concrete tower of a single cable plane cable‐stayed bridge is considered. The strut‐and‐tie model (STM) of the pylon wall subject to the vertical components of one single cable force was derived. Based on the minimum strain energy principle, an equation for predicting the bursting force was given. Then, the STMs of a concrete pylon with two cable forces with different vertical distances between cables were proposed. A series of equations for predicting the bursting force in different STMs were presented. The STMs of a concrete pylon with multiple cables were subsequently obtained from the STM for two cable forces. The analysis results show that the vertical distance between cables has a great influence on the STM configuration of the tower. When the cable distance is less than 0.7 times the width of the tower wall, the bursting force is larger than that when the cable distance is larger than 0.7 times the width of the tower wall. This study was expected to provide a reference in the design and applications of pylons of concrete cable‐stayed bridges.

Construction of strut‐and‐tie models for members under complex stress states based on topology optimization

AbstractThe construction of strut‐and‐tie models (STMs) is the key, but also the difficulty when the model is used to describe the force mechanism and guide the reinforcement layout design of concrete disturbed regions (D‐regions). Topology optimization is a promising way to guide STMs construction. Different from the existing construction methods of predetermining nodes, the angle of inclination of the truss elements is first determined to ensure that it is consistent with that of the principal stresses in a 2D finite element model of the structure. The constructed model can well reflect the force transmission path of structural members, and it is better than the existing methods when it is evaluated through the principle of minimum strain energy. To verify the validity of the STM, a reinforcement layout scheme is adopted completely according to the position of the tension ties. On this basis, another reinforcement layout scheme adds additional transverse reinforcements in the bottle‐shaped stress field. The nonlinear finite element comparative analysis of an irregular deep beam designed by the two schemes is carried out. The results show that the two ultimate loads are close. Brittle failure occurs in the former, while the latter has higher deformability and eventually ductile failure occurs.

Stability Index of Surrounding Rock during Deep Rock Excavation Considering Energy Release Speed

Rockburst is a kind of dynamic rock failure process that is easily induced by the excavation of a high-stress rock mass. However, from an energy perspective, the existing indexes for rockburst tendency have a limitation in that they do not consider the energy release speed. In this study, energy release effectiveness was proposed based on the local energy release rate while considering the influence of the energy release speed. The index can evaluate the stability of surrounding rock during the excavation of high-stress rock. The index can be obtained by recording the strain energy density of every element in the model during excavation and identifying the maximum strain energy density (Eimax), the minimum strain energy density (Eimin), the maximum time (timax), and the minimum time (timin) to calculate energy release speed and energy release effectiveness. A case study of the excavation of an experimental tunnel, namely, the URL of AECL, was adopted to validate the index. The results indicated that the proposed index can clearly identify the location and strength of the impact tendency area, and it can be effectively applied to the stability analysis during the excavation of deep tunnels.

Topology optimization for the design of a 3D-printed rotating shaft balance

Rotating shaft balances (RSBs) are devices that are used to measure rotor blade forces and moments of wind tunnel models during wind tunnel tests. The design of an RSB can be challenging, because it has to comply with many and sometimes contradicting requirements such as high stiffness and high strain gauge bridge outputs. The manufacturing of a conventional RSB consists of different subsequent steps, which can be time consuming, expensive and associated with many risks. Therefore, in this work, the authors investigate if a RSB can be designed by topology optimization and manufactured by 3D printing. A topology optimization method was developed with as design objective the minimization of strain energy with constraints for the volume of the RSB’s midsection, defined stresses at strain gauge locations used for the measurement of axial force and torque and an overhang constraint for additive manufacturing. The optimal preliminary design found by topology optimization was translated into a final printable design with the highest bridge sensitivity for axial force and torque, sufficient output for in-plane forces and moments and an acceptable safety factor on strength for combined loads. After adding extra supports required for printing, the RSB was successfully printed in metal by the laser powder bed fusion process, resulting in a product without external defects. The same topology optimization and manufacturing method can potentially be used for other balance types, leading to a reduction in total lead time and manufacturing costs while increasing the design freedom.