In-plane Constraint Research Articles

Effect of in-plane strain anisotropy on (011) epitaxial BaTiO3 and PbTiO3 thin films

Misfit strain phase diagrams of single-domain (011) epitaxial BaTiO3 and PbTiO3 thin films are computed using a thermodynamic phenomenological approach. In the case of (001) epitaxial films, the two orthogonal in-plane misfit strains are equivalent. For (011) epitaxial films, however, the two substrate constraints exert quantitatively different influences due to crystal anisotropy. Effects of preferential strain relaxation and arbitrary in-plane strains are investigated, and similarity and contrast of BaTiO3 and PbTiO3 phase diagrams are revealed. Impact of anisotropy of in-plane constraint on polarization, dielectric and piezoelectric properties is explored, and the calculated structural transitions and out-of-plane lattice strain are compared with relevant theoretical and experimental data reported in the literature.

Micromechanical Analysis of In-Plane Constraint Effect on Local Fracture Behavior of Cracks in the Weakest Locations of Dissimilar Metal Welded Joint

In this work, a set of GTN (Gurson–Tvergaard–Needleman) parameters of the Alloy52M dissimilar metal welded joint (DMWJ) have been calibrated, and a micromechanical analysis of in-plane constraint effects on the local fracture behavior of two cracks, which located in the weakest regions of the DMWJ, has been investigated by the local approach based on the GTN damage model. The results show that the partition of the material and the variation of the q 2 parameter make the J-resistance curves obtained by numerical simulations close to the experimental values. The numerical J-resistance curves and crack growth paths are consistent with the experiment results, which show that the GTN damage model can incorporate the in-plane constraint effect. Furthermore, after the stress, strain and damage fields at the crack tip during the crack propagation process have been calculated, and the change of the J-resistance curves, crack growth paths and fracture mechanism with in-plane constraint have been analyzed.

Deflection behaviour of corrosion crack growth in the heat affected zone of CrNiMoV steel welded joint

Stress corrosion cracking (SCC) growth tests in heat affected zone (HAZ) of 25Cr2Ni2MoV steel welded joint were conducted in 3.5wt.% NaCl solution at 180°C. The deflection of SCC towards the hard side of HAZ was observed interestingly, which was ascribed to the combined effect of the graded mechanical and electrochemical properties in HAZ. In addition, the initiation of SCC deflection was related to the crack-tip in-plane constraint. Through the specimen thickness, higher crack-tip out-of-plane constraint on the mid-thickness plane caused a preferential SCC deflection compared to that on the surface.

Numerical Analysis of the Influence of In-Plane Constraints on the Crack Tip Opening Displacement for SEN(B) Specimens Under Predominantly Plane Strain Conditions

This paper presents a numerical analysis of the relationship between in-plane constraints and the crack tip opening displacement (CTOD) for single-edge notched bend (SEN(B)) specimens under predominantly plane strain conditions. It provides details of the numerical model and discusses the influence of external load and in-plane constraints on the CTOD. The work also reviews methods for determining the CTOD. The new formula proposed in this paper can be used to estimate the value of the coefficient <i>dn</i> as a function of the relative crack length, the strain hardening exponent and the yield strength - <i>dn</i>(<i>n</i>, <i>σ0</i>/E, <i>a/W</i>), with these parameters affecting the level of in-plane constraints. Some of the numerical results were approximated using simple mathematical formulae.

Quantifying the creep crack-tip constraint effects using a load-independent constraint parameter Q*

In this work, a load-independent creep constraint parameter Q* was introduced, and its load-independence was confirmed by 3D finite element analyses of six different cracked specimens. A fixed distance r=0.2mm ahead of crack tips was chosen to define the Q*. In addition, the parameter Q* was used to quantify the in-plane constraint induced by crack depths, specimen widths and loading configurations and the constraint effects induced by specimen thicknesses. The results revealed that the values of Q* increased with increasing the crack depths (a/W ≤0.5) and specimen thicknesses and decreased with increasing the width-thickness ratio W/B of specimens. Furthermore, the highest constraint level occurred in the CT specimen while the lowest occurred in the CCT specimen.

Voids Nucleation at Inclusions of Various Shapes in Front of the Crack in Plane Strain

Abstract An analysis is presented of the stress field in and around inclusions of various shapes. Results were obtained by the finite element method. Inclusions were located within elementary cells located at the centre of the specimen next to the crack front. The influence of an in-plane constraint on the stress distribution was tested.

Prediction of creep crack initiation behaviour in 316H stainless steel using stress dependent creep ductility

The creep crack initiation behaviour of Type 316H stainless steel at 550°C has been predicted by implementing a stress dependent creep ductility and average creep strain rate model in finite element analyses. Simulations were performed on five specimen geometries: C(T), CS(T), DEN(T), M(T) and SEN(T). The predicted results have been characterised using the C* fracture mechanics parameter and the short-term, long-term and transition creep crack initiation trends are predicted for each of the specimen geometries examined. The prediction results have been validated through comparison with experimental data available in the literature. The predicted short-term and long-term creep crack initiation trends have also been compared with NSW prediction lines. The predicted results, from each specimen geometry, are compared to each other and the differences in crack initiation trends have been discussed in terms of the specimen geometry, in-plane constraint and stress level effects on the creep crack initiation behaviour of the material. A mesh sensitivity analysis has also been performed to find the optimum mesh size for performing crack initiation simulations.

Unified correlation of geometry and material constraints with creep crack growth rate of welded joints

The constraint parameter Ac based on crack-tip equivalent creep strain and creep crack growth rates of two interface cracks in welded joint C(T) specimens with different in-plane and out-of-plane constraints have been calculated and analyzed. The results show that the parameter Ac can characterize both geometry constraint (in-plane and out-of-plane constraints) and material constraint in welded joints. Based on Ac, a unified correlation of geometry and material constraints with creep crack growth rates of welded joints can be established, and it may be used in accurate creep life assessments for welded components with various in-plane, out-of-plane and material constraint levels.

Unified correlation of in-plane and out-of-plane creep constraints with creep crack growth rate

In this paper, the equivalent creep strain distributions ahead of crack tips in SEN(B), SEN(T) and M(T) specimens with different in-plane and out-of-plane constraints were calculated by extensive finite element analyses, and the creep crack growth (CCG) rates of these specimens were simulated over a wide range of C* by using stress dependent creep ductility and strain rate model in a ductility exhaustion based damage model. The capability and applicability of the constraint parameter Ac based on crack-tip equivalent creep strain for characterizing both in-plane and out-of-plane creep crack-tip constraints and establishing a unified correlation with CCG rate of a steel were investigated. The results show that with increasing constraints, the CCG rate increases, and the effect of out-of-plane constraint on CCG rate is more obvious than that of in-plane constraint. The CCG rate of high constraint specimen geometry (such as SEN(B)) is more sensitive to the out-of-plane and in-plane constraints than that of low constraint specimen geometry (such as M(T)). The parameter Ac is a unified characterization parameter of in-plane and out-of-plane creep constraints for the different specimen geometries. Base on the parameter Ac, the unified correlation formulas of in-plane and out-of-plane constraints with CCG rate of the steel have been obtained, and they are independent on the choices of the standard specimen. The unified correlation formulas may be used in constraint-dependent CCG life assessments of high-temperature components (such as pressure vessels and pipes) with any in-plane and out-of-plane constraint levels.

Buckling and vibration behavior of a non-uniformly heated isotropic cylindrical panel

This study attempts to address the buckling and free vibration characteristics of an isotropic cylindrical panel subjected to non-uniform temperature rise using numerical approach. Finite element analysis has been used in the present study. The approach involves three parts, in the first part non-uniform temperature field is obtained using heat transfer analysis, in the second part, the stress field is computed under the thermal load using static condition and, the last part, the buckling and pre-stressed modal analysis are carried out to compute critical buckling temperature as well as natural frequencies and associated mode shapes. In the present study, the effect of non-uniform temperature field, heat sink temperatures and in-plane boundary constraints are considered. The relation between buckling temperature under uniform and non-uniform temperature fields has been established. Results revealed that decrease (Case (ii)) type temperature variation field influences the fundamental buckling mode shape significantly. Further, it is observed that natural frequencies under free vibration state, decreases as temperature increases. However, the reduction is significantly higher for the lowest natural frequency. It is also found that, with an increase in temperature, nodal and anti-nodal positions of free vibration mode shapes is shifting towards the location where the intensity of the heat source is high and structural stiffness is low.

A Combined In Vitro Imaging and Multi-Scale Modeling System for Studying the Role of Cell Matrix Interactions in Cutaneous Wound Healing.

Many cell types remodel the extracellular matrix of the tissues they inhabit in response to a wide range of environmental stimuli, including mechanical cues. Such is the case in dermal wound healing, where fibroblast migrate into and remodel the provisional fibrin matrix in a complex manner that depends in part on the local mechanical environment and the evolving multi-scale mechanical interactions of the system. In this study, we report on the development of an image-based multi-scale mechanical model that predicts the short-term (24 hours), structural reorganization of a fibrin gel by fibroblasts. These predictive models are based on an in vitro experimental system where clusters of fibroblasts (i.e., explants) were spatially arranged into a triangular geometry onto the surface of fibrin gels that were subjected to either Fixed or Free in-plane mechanical constraints. Experimentally, regional differences in short-term structural remodeling and cell migration were observed for the two gel boundary conditions. A pilot experiment indicated that these small differences in the short-term remodeling of the fibrin gel translate into substantial differences in long-term (4 weeks) remodeling, particularly in terms of collagen production. The multi-scale models were able to predict some regional differences in remodeling and qualitatively similar reorganization patterns for the two boundary conditions. However, other aspects of the model, such as the magnitudes and rates of deformation of gel, did not match the experiments. These discrepancies between model and experiment provide fertile ground for challenging model assumptions and devising new experiments to enhance our understanding of how this multi-scale system functions. These efforts will ultimately improve the predictions of the remodeling process, particularly as it relates to dermal wound healing and the reduction of patient scarring. Such models could be used to recommend patient-specific mechanical-based treatment dependent on parameters such as wound geometry, location, age, and health.

An optimized nano-positioning stage for Bristol’s Transverse Dynamic Force Microscope

Abstract: This paper presents the design process for the optimisation of a nano-precision actuation stage for a Transverse Dynamic Force Microscope (TDFM). A TDFM is an advanced type of Atomic Force microscope (AFM) that does not contact the specimen and therefore has potential for increased accuracy and decreased damage to the specimen. The nano-precision stage actuates in a horizontal plane within a region of 1 μm×1μm and with a resolution of 0.3 nm. The non-contact TDFM has been developed at Bristol University for the precise topographical mapping of biological and non-biological specimens in ambient conditions. The design objective was to maximise positional accuracy during high speed actuation. This is achieved by minimising vibrations and distortion of the stage during actuation. Optimal performance was achieved through maximising out-of-plane stiffness through shape and material selection, as well optimisation of the anchoring system. The design was subject to constraints including an in-plane stiffness constraint, space constraints and design features relating to the laser interferometry position sensing system and subsequent controller design.

Tether deployment with in-plane angular and explicit velocity constraints by barrier Lyapunov function

Space tethers have been used for many space applications for decades. However, how to deploy a tethered system in a non-overshooting and stable way is still an unsolved issue up to now. Especially for passive deployment devices where positive deploy velocity is an essential requirement. In addition, in-plane angular amplitude is another issue that we should restrict to prevent tether become slack when it transgress 45°. This paper proposes a new control method to satisfy the two main constraints. First, we use a modified barrier Lyapunov Function method to design a deploy trajectory, which could ensure the in-plane angular stable and restrict into a small range as well as a positive deploy velocity. Second, we employ a feedback linearisation to realise a non-overshooting tracking. Simulations demonstrate that the scenario is successful in keeping a small in-plane angular within 0.25 radian, and positive deploy velocity and tension, meanwhile guaranteeing the non-overshooting tether length state.

Combined load buckling for cylindrical shells based on a symplectic elasticity approach

Buckling behavior of cylindrical shells subjected to combined pressure, torsion and axial compression is presented by employing a symplectic method. Both symmetric and non-symmetric boundary conditions are considered. Hamiltonian canonical equations are established by introducing four pairs of dual variables. Then, solution of fundamental equations is converted into a symplectic eigenvalue problem. It is concluded that the influence of pressure on buckling solutions is more significant than that due to compressive load, in particular for a longer external pressured cylindrical shell. Besides, buckling loads and circumferential wavenumbers can be reduced greatly by relaxed in-plane axial constraints.

The influence of the out-of- and in-plane constraint on fracture toughness of high strength steel in the ductile to brittle transition temperature range

In the paper the analytical formulae to predict the fracture toughness are proposed. They take into account the influence of in- and out-of-plane constraints. The formula which takes into account the out-of-plane constraint contains the plane strain JIC and Guo’s Tz parameter. Alternatively the ratio of the effective to yield stress can be used. The influence of the in-plane constraint can be assessed using JIC and O’Dowd’s, and Shih’s Q parameter. The theoretical predictions were verified by the results of the experimental program. A good agreement between the theoretical and experimental results is observed.

Formability optimisation of fabric preforms by controlling material draw-in through in-plane constraints

A genetic algorithm is coupled with a finite element model to optimise the arrangement of constraints for a composite press-forming study. A series of springs are used to locally apply in-plane tension through clamps to the fibre preform to control material draw-in. The optimisation procedure seeks to minimise local in-plane shear angles by determining the optimum location and size of constraining clamps, and the stiffness of connected springs. Results are presented for a double-dome geometry, which are validated against data from the literature. Controlling material draw-in using in-plane constraints around the blank perimeter is an effective way of homogenising the global shear angle distribution and minimising the maximum value. The peak shear angle in the double-dome example was successfully reduced from 48.2° to 37.2° following a two-stage optimisation process.

Numerical Analysis of Constraint and Strength Mismatch Effects on Local Fracture Resistance of Bimetallic Joints

In this paper, the finite element method (FEM) based on GTN model was used to investigate the in-plane/out-of-plane constraint and strength mismatch effects on local fracture resistance of A508/Alloy52Mb bimetallic joint. TheJ-resistance curves, crack growth paths and local stress-stain distributions in front of crack tips were calculated for cracks with different constraints and strength mismatches. The results show that the local fracture resistance of the interface crack in this joint is sensitive to constraint and strength mismatch effects. With increasing in-plane constraint (crack deptha/W), out-of-plane constraint (specimen thicknessB) and strength mismatch degree, the plastic strain and stress triaxiality around crack tip increase, and the corresponding crack growth resistance decreases. The crack with strength mismatch factorM=1 displays a markedly higher crack growth resistance than the other cracks withM>1 andM<1. It also has been found that there is an interaction between in-plane/out-of-plane constraint and strength mismatch for the bimetallic joint. With increasing in-plane/out-of-plane constraint, strength mismatch effect on fracture toughness becomes weaken. For accurate and reliable safety design and failure assessment of the bimetallic joint structures, the effects of constraint and strength mismatch on local fracture resistance need to be considered.

Adaptive mechanical properties of topologically interlocking material systems

Topologically interlocked material systems are two-dimensional granular crystals created as ordered and adhesion-less assemblies of unit elements of the shape of platonic solids. The assembly resists transverse forces due to the interlocking geometric arrangement of the unit elements. Topologically interlocked material systems yet require an external constraint to provide resistance under the action of external load. Past work considered fixed and passive constraints only. The objective of the present study is to consider active and adaptive external constraints with the goal to achieve variable stiffness and energy absorption characteristics of the topologically interlocked material system through an active control of the in-plane constraint conditions. Experiments and corresponding model analysis are used to demonstrate control of system stiffness over a wide range, including negative stiffness, and energy absorption characteristics. The adaptive characteristics of the topologically interlocked material system are shown to solve conflicting requirements of simultaneously providing energy absorption while keeping loads controlled. Potential applications can be envisioned in smart structure enhanced response characteristics as desired in shock absorption, protective packaging and catching mechanisms.

Quantifying the constraint effect induced by specimen geometry on creep crack growth behavior in P92 steel

In this paper, the effect of the specimen geometry on the creep crack growth behavior in P92 steel was quantified and six different types of cracked specimens (including C-ring in tension CS(T), compact tension C(T), single notch tension SEN(T), single notch bend SEN(B), middle tension M(T), and double edge notch bend tension DEN(T)) were employed. Results revealed that the creep crack growth rate against C⁎ relations varied with changing specimen geometry. For a given C⁎ value, C(T) and CS(T) showed the highest crack growth rates, which were three times as the lowest crack growth rates in M(T). This revealed that distinctions in specimen geometry influenced the in-plane constraint level ahead of crack tip. Moreover, constraint parameter Q was introduced to quantify the in-plane constraint. During the creep crack propagation, the distributions of Q varied as specimen geometry changed. The specimen order in terms of Q values from high to low was CS(T), C(T), DEN(T), SEN(B), SEN(T) and M(T), which basically represented the constraint level in these specimens.

Investigation of constraint and warm prestressing effects by means of a local approach to fracture

Brittle cleavage fracture, constraint effects as well as warm prestressing (WPS) effects play important roles in structural integrity analysis. A local approach to fracture, i.e. the σ∗−A∗ model is used to study the constraint and WPS effects on material toughness. The crack depth and loading determine the in-plane constraint while the thickness at the crack tip has an important impact on the out-of-plane constraint. Residual stress contributes to the WPS effect, whereas the increase of fracture toughness is not completely attributed to the residual stress. The magnitudes of preloading and unloading and the reloading temperature determine the increased fracture toughness.