Stress-free State Research Articles

Experimental Study on Thermal Expansion Behavior of Concrete under Three-Dimensional Stress

Concrete is widely used in underground engineering and bears three-dimensional stress transmitted by overlying load. When a fire occurs, the thermal expansion of concrete structure under such stress state is different from that under stress-free state. For this purpose, a self-developed real-time high-temperature true triaxial test system was applied to investigate the thermal expansion behavior of concrete under three-dimensional stress state. The thermal expansion strain of concrete under the three-dimensional stress undergoes strain increasing and strain stabilizing stages. At 600°C, the maximum thermal expansion strain of concrete under the three-dimensional stress is 0.75%. The average coefficient of thermal expansion of concrete under three-dimensional stress condition was then calculated, and its value reaches the minimum of 8.68 × 10−6/°C at 200°C and the maximum of 13.41 × 10−6/°C at 500°C. Comparing the coefficient of thermal expansion of concrete under stress-free condition given by Eurocode, it is found that the three-dimensional stress has an obvious restraint on the thermal expansion of concrete. The research results can provide theoretical basis for the stability analysis of underground engineering concrete structures under high-temperature environment.

Calculating the gravity-free shape of sheet metal parts

This paper presents an iterative finite element (FE)–based method to calculate the gravity-free shape of nonrigid parts from an optical measurement performed on a non-over-constrained fixture. Measuring these kinds of parts in a stress-free state is almost impossible because deflections caused by their weight occur. To solve this problem, a simulation model of the measurement is created using available methods of reverse engineering. Then, an iterative algorithm calculates the gravity-free shape. The approach does not require a CAD model of the measured part, implying the whole part can be fully scanned. The application of this method mainly addresses thin, unstable sheet metal parts, like those commonly used in the automotive or aerospace industry. To show the performance of the proposed method, validations with simulation and experimental data are presented. The shown results meet the predefined quality goal to predict shapes within a tolerance of ± 0.05 mm measured in surface normal direction.

Effects of curvature on the propagation of undulatory waves in lower dimensional elastic materials

The mechanics of lower dimensional elastic structures depends strongly on the geometry of their stress-free state. Elastic deformations separate into in-plane stretching and lower energy out-of-plane bending deformations. For elastic structures with a curved stress-free state, these two elastic modes are coupled within linear elasticity. We investigate the effect of that curvature-induced coupling on wave propagation in lower dimensional elastic structures, focusing on the simplest example-a curved elastic rod in two dimensions. We focus only on the geometry-induced coupling between bending and longitudinal (in-plane) strain that is common to both rods in two dimensions and to elastic shells. We find that the dispersion relation of the waves becomes gapped in the presence of finite curvature; bending modes are absent below a frequency proportional to the curvature of the rod. By studying the scattering of undulatory waves off regions of uniform curvature, we find that undulatory waves with frequencies in the gap associated with the curved region tunnel through that curved region via conversion into compression waves. These results should be directly applicable to the spectrum and spatial distribution of phonon modes in a number of curved rod-like elastic solids, including carbon nanotubes and biopolymer filaments.

Mechanics and Energetics of Electromembranes.

The recent discovery of electroactive polymers has shown great promises in the field of soft robotics and was logically followed by experimental, numerical, and theoretical developments. Most of these studies were concerned with systems entirely covered by electrodes. However, there is a growing interest for partially active polymers, in which the electrode covers only one part of the membrane. Indeed, such actuation can trigger buckling instabilities and so represents a route toward the control of three-dimensional shapes. Here, we study theoretically the behavior of such partially active electroactive polymer. We address two problems: (1) the electrostatic elastica including geometric nonlinearities and partially electroactive strip using a variational approach. We propose a new interpretation of the equations of deformation, by drawing analogies with biological growth, in which the effect of the electric voltage is seen as a change in the reference stress-free state. (2) We explain the nature of the distribution of electrostatic forces on this simple system, which is not trivial. In particular, we find that edge effects are playing a major role in this problem.

Non-dimensional thermoelastic model of a compound annular cylinder in a stress-free state with internal heat generation

A non-dimensional, axisymmetric, thermal-stress model for a three-layer cylinder with internal heating has been developed. Such a geometry is encountered in an annular target for isotope production. The middle cylinder is the heat generating source with an assumed thermal expansion coefficient that is smaller than that of the other two cylinders enclosing it. Hence, the development of the solution is based on the assumption that interfacial separation occurs at the interface of the middle cylinder and the outer cylinder, while contact is reinforced between the middle cylinder and the inner cylinder. The commercial finite element code Abaqus FEA is used to obtain a numerical model which is validated using the developed analytical solution. The non-dimensional analytical solution has been presented in a simplified, generalized form, and can be applied to either of the cylinders by adjusting a few parameters. The non-dimensional variable groupings allow physical insight into how the stresses and temperature distributions evolve. A detailed solution procedure along with a discussion of the results has been provided.

The stress–immunity axis in shellfish

It is a difficult task to describe what constitutes a ‘healthy’ shellfish (e.g., crustacean, bivalve). Visible defects such as discolouration, missing limbs or spines, fouling, lesions, and exoskeletal fractures can be indicative of underlying issues, senescence, or a ‘stressed’ animal. The absence of such symptoms is not evidence of a disease-free or a stress-free state. Now, more than ever, aquatic invertebrates must cope with acute and chronic environmental perturbations, such as, heatwaves and cold shocks, xenobiotic contaminants, intoxication events, and promiscuous pathogens expanding their host and geographic ranges. With that in mind, how does one determine the extent to which shellfish become stressed in situ (natural) or in cultured (artificial) settings to enhance disease susceptibility? Many biomarkers – predominantly biochemical and cellular measures of shellfish blood (haemolymph) – are considered to gauge immunosuppression and immunocompetence. Such measures range from immune cell (haemocyte) counts to enzymic activities and metabolite quantitation. Stressed invertebrates often reflect degraded conditions of their ecosystems, referred to as environmental indicators.We audit briefly the broad immune functions of shellfish, how they are modulated by known and emerging stressors, and discuss these concepts with respect to neuroendocrinology and immunotoxicology. We assert that chronic stress, alone or in combination with microbial, chemical and abiotic factors, increases the risk of infectious disease in shellfish, exacerbates idiopathic morbidity, and reduces the likelihood of recovery. Acute stress events can lead to immunomodulation, but these effects are largely transient. Enhancing our understanding of shellfish health and immunity is imperative for tackling losses at each stage of the aquatic food cycle and disease outbreaks in the wild.

Triboelectric and Piezoelectric Nanogenerators for Future Soft Robots and Machines.

SummaryThe triboelectric nanogenerator (TENG) and piezoelectric nanogenerator (PENG) are two recently developed technologies for effective harvesting of ambient mechanical energy for the creation of self-powered systems. The advantages of TENGs and PENGs which include large open-circuit output voltage, low cost, ease of fabrication, and high conversion efficiency enable their application as new flexible sensors, wearable devices, soft robotics, and machines. This perspective provides an overview of the current state of the art in triboelectric and piezoelectric devices that are used as self-powered sensors and energy harvesters for soft robots and machines; hybrid approaches that combine the advantages of both mechanisms are also discussed. To improve system performance and efficiency, the potential of providing self-powered soft systems with a degree of multifunctionality is investigated. This includes optical sensing, transparency, self-healing, water resistance, photo-luminescence, or an ability to operate in hostile environments such as low temperature, high humidity, or high strain/stretch. Finally, areas for future research directions are identified.

Stress evolution in different growth mechanism of GaN grown by Na-flux method

The study found that homoepitaxial Na-flux GaN has a large stress at the interface, and the stress is released to a certain extent within 50 μm in the growth direction of the Na-flux GaN. After passing through the columnar growth region, the Na-flux GaN tends to a stress-free state finally. The columnar growth mode is produced by GaN island growth, the islands nucleate and coalescence to produce tensile stress. The Na-flux GaN undergoes a columnar growth to generate tensile stress, which offsets the residual compressive stress at the interface, which is conducive to stress release.

Geometrically nonlinear modelling of pre-stressed viscoelastic fibre-reinforced composites with application to arteries.

Mechanical behaviour of pre-stressed fibre-reinforced composites is modelled in a geometrically exact setting. A general approach which includes two different reference configurations is employed: one configuration corresponds to the load-free state of the structure and another one to the stress-free state of each material particle. The applicability of the approach is demonstrated in terms of a viscoelastic material model; both the matrix and the fibre are modelled using a multiplicative split of the deformation gradient tensor; a transformation rule for initial conditions is elaborated and specified. Apart from its simplicity, an important advantage of the approach is that well-established numerical algorithms can be used for pre-stressed inelastic structures. The interrelation between the advocated approach and the widely used "opening angle" approach is clarified. A full-scale FEM simulation confirms the main predictions of the "opening angle" approach. A locking effect is discovered: in some cases the opening angle of the composite is essentially smaller than the opening angles of its individual layers. Thus, the standard cutting test typically used to analyse pre-stresses does not carry enough information and more refined experimental techniques are needed.

Compliant morphing structures from twisted bulk metallic glass ribbons

In this work, we investigate the use of pre-twisted metallic ribbons as building blocks for shape-changing structures. We manufacture these elements by twisting initially flat ribbons about their (lengthwise) centroidal axis into a helicoidal geometry, then thermoforming them to make this configuration a stress-free reference state. The helicoidal shape allows the ribbons to have preferred bending directions that vary throughout their length. These bending directions serve as compliant joints and enable several deployed and stowed configurations that are unachievable without pre-twist, provided that compaction does not induce material failure. We fabricate these ribbons using a bulk metallic glass (BMG), for its exceptional elasticity and thermoforming attributes. Combining numerical simulations, an analytical model based on a geometrically nonlinear plate theory and torsional experiments, we analyze the finite-twisting mechanics of various ribbon geometries. We find that, in ribbons with undulated edges, the twisting deformations can be better localized onto desired regions prior to thermoforming. Finally, we join multiple ribbons to create deployable systems with complex morphing attributes enabled by the intrinsic chirality of our twisted structural elements. Our work proposes a framework for creating fully metallic, yet compliant structures that may find application as elements for space structures and compliant robots.

Periodic crack problems for an elastic layer

The problems of periodic mode I 3 D cracks for an elastic layer are reduced to an integro-differential equation (IDE). The principal part of the IDE is the same as in the classical Griffith problem for one crack in an elastic full space. The periodic system of elliptic cracks, featuring equal spaces between neighboring cracks, lies in the middle plane of the layer. Each crack is parallel to the layer’s faces. Four types of boundary conditions are considered on the layer’s faces (sliding or rigid support, stress-free state, sliding support in between elastic layers). The regular asymptotic method has been applied to solving the problems as it proves effective for some fairly big spaces between cracks as well as for relatively thick layers. The stress intensity factor (SIF) has been calculated for a variety of geometric and mechanical parameters. It was compared to that for the well-known case of a single crack in a layer. It has been shown that the SIF for the crack system can be smaller or greater than that for a single crack depending on the boundary conditions on the layer’s faces.

On the recovery of the stress-free configuration of the human cornea

Purpose: The geometries used to conduct numerical simulations of the biomechanics of the human cornea are reconstructed from images of the physiological configuration of the system, which is not in a stress-free state because of the interaction with the surrounding tissues. If the goal of the simulation is a realistic estimation of the mechanical engagement of the system, it is mandatory to obtain a stress-free configuration to which the external actions can be applied.
 Methods: Starting from a unique physiological image, the search of the stress-free configuration must be based on methods of inverse analysis. Inverse analysis assumes the knowledge of one or more geometrical configurations and, chosen a material model, obtains the optimal values of the material parameters that provide the numerical configurations closest to the physiological images. Given the multiplicity of available material models, the solution is not unique.
 Results: Three exemplary material models are used in this study to demonstrate that the obtained, non-unique, stress-free configuration is indeed strongly dependent on both material model and on material parameters.
 Conclusion: The likeliness of recovering the actual stress-free configuration of the human cornea can be improved by using and comparing two or more imaged configurations of the same cornea.

Post-fire mechanical properties of stainless steel cables

During the heating process of a fire test, most test specimens are in a stress-free state, while the components of the actual structures are often in a complex state of stress, particularly for pre-stressed members such as steel cables. To reflect the actual fire conditions of stainless steel cables and explore the effects of stress levels on the mechanical properties of stainless steel cables after high temperatures, this study examines the residual mechanical properties of a stainless steel cable after high temperatures. A fire test on stainless steel cables at different stress levels was conducted, and subsequently, the static tensile test at room temperature (30°C) was conducted for the specimens after firing and after natural air cooling. The elastic modulus, tensile strength, yield strength, fracture strain, and stress-strain curves of the stainless steel cables under different temperature-stress conditions were obtained. The mechanical properties of stainless steel cables after a high temperature were compared with those of carbon steel cables and other stainless steel materials. The equations to predict the mechanical properties of a stainless steel cable after a high temperature are provided, and it can provide a reference for the safety assessment and replacement of pre-stressed structures after a fire.

Validation and Optimization of Calculated Stress Fields in Double-Mold Optoelectronics Sensor Packaging

Thermomechanical modeling of a new double-overmolded optical sensor package, comprising a highly filled, as well as an unfilled, strongly thermally expanding transfer molding compound, is presented. Materials’ characterization of the polymers using thermal, thermomechanical, dynamic, and optical correlation methods was used to set up finite element models of the three major steps in the assembly packaging process. The results of the simulation were validated by in-plane stress determination using a piezoresistive integrated circuit measured at various temperatures. In addition, the overall package substrate warpage was optically characterized while loading the sample on a hot plate. Agreement between the measurement and the simulation was only found when the stress-free state of the polymers was set to be at the curing-onset temperature. The results obtained are compared with different levels of complexity on materials’ characterization and constitutive modeling and could finally be used for sensitivity analysis of the sensor package design. A thicker and more compliant transparent molding compound in this package was found to reduce the stresses that could cause delamination.

Influence of External Interface Normal Stress on the Growth of Cu–Sn IMC During Aging

A U-shape clamp was designed to apply stress perpendicular to the interface of Cu/Sn/Cu solder joints, and its influence on the growth behavior of Cu–Sn intermetallic compound (IMC) during thermal aging at 150 °C was investigated. The results show that compared with the sample at general stress-free state, the growth rate of IMC under compression is faster, while that under tension is slower. Moreover, the interface between IMC and Sn is smoother under compressive stress, and the corresponding IMC grains are smaller and more uniform than that under tensile stress. According to the growth kinetic analysis, the growth of IMC under general, compressive and tensile states is all controlled by the combination of grain boundary diffusion and volume diffusion with a similar growth exponent (n ≈ 0.4). However, external stress can affect the Ostwald ripening process of grain growth, causing a change of grain size and grain boundary density in the IMC layer. As a result, the IMC growth behavior at the interface of the solder joint will be affected by the applied external normal stress.

Effect of annealing temperature on texture and residual stress of Ti-6Al-4V alloy seamless tubing processed by cold rotary swaging

The thin-walled seamless Ti-6Al-4V alloy tubing was prepared by cold rotary swaging (RS) with a 40% wall reduction. The microstructure, texture and residual stress of the tubing samples under different annealing temperatures were investigated. The results show that the grains of the tubing samples after RS are obviously refined and streamlined. The maximum density level displayed in the cut of orientation distribution function (ODF) increases from 4.51 to 8.32, with a basal tilt angle of 10° around the radial direction of the tubing, which indicates that the radial texture of the Ti-6Al-4V alloy tubing become stronger after RS. Additionally, the post-swaging annealing at 400 °C and 500 °C for 2.5 h were adopted to relieve the residual stress of the tubing samples. The former can just relieve at most 80% of the residual stress, while the latter can relieve 97% of the residual stress to achieve an almost stress-free state. Hence, it is thought that the annealing at 500 °C can achieve the better effect to relief the residual stress.

Modeling of subsurface ceramic inclusions in metallic matrices

All engineering materials have the potential to contain inhomogeneities that can act as initiators for fatigue cracks during cyclic loading. One class of inhomogeneity that can occur as a result of the processes used to create metallic materials is a ceramic inclusion, typically resulting from the raw material contamination during the melting process. This article examines the predicted behavior of hard ceramic inclusions in a nickel-base superalloy metallic matrix. Compressive residual stresses are created in the inclusion during cool down from a stress-free state at high temperature. The influence of the proximity of the inclusion to the surface of the matrix material is examined, together with the impact of subsequent uniaxial loading on the stress field in the inclusion and in the surrounding material. The stress field in the ceramic inclusion is observed to transition from compressive to tensile as a function of the proximity of the inclusion to the surface of the material and the applied uniaxial stress field. For deep subsurface inclusions, the uniaxial stress field required to achieve a tensile stress in the inclusion is close to the yield stress of the material. The sensitivity of this critical stress to material cyclic hardening behavior and to the temperature difference between the stress-free state and the operating state is also explored. The significance of these modeling results is discussed in terms of the sensitivity of nickel-base superalloys to crack formation and growth from ceramic inclusions and hence the impact on probabilistic fatigue life assessments of the presence, location and size of the ceramic inclusions.

Deformation of stainless steel cables at elevated temperature

The deformation of stainless steel cables at elevated temperatures is an important consideration for the design of fire resistant pre-stressed spatial structures. In this paper, by conducting extensive experiments on a number of specimens, the thermal expansion under a stress-free state, the deformation under thermo-mechanical coupling state in transient heating stage, and the creep deformation in constant temperature stage of stainless cables subjected to elevated temperature were studied experimentally. A correlation for the thermal expansion coefficient of the stainless steel cables in the range of 30–600 °C was obtained. In addition, an equation relating the deformation of the cables and the temperature and initial stress under the thermo-mechanical coupling state in the heating stage was proposed. Furthermore, the relationship between the parameters of the Field & Field creep model and the temperature was derived for the stainless steel cables.

Level-set topology optimization considering nonlinear thermoelasticity

At elevated temperature environments, elastic structures experience a change of the stress-free state of the body that can strongly influence the optimal topology of the structure. This work presents level-set based topology optimization of structures undergoing large deformations due to thermal and mechanical loads. The nonlinear analysis model is constructed by multiplicatively decomposing thermal and mechanical effects and introducing an intermediate stress-free state between the undeformed and deformed coordinates. By incorporating the thermoelastic nonlinearity into the level-set topology optimization scheme, wider design spaces can be explored with the consideration of both mechanical and thermal loads. Four numerical examples are presented that demonstrate how temperature changes affect the optimal design of large-deforming structures. In particular, we show how optimization can manipulate the material layout in order to create a counteracting effect between thermal and mechanical loads, even up to a degree that buckling and snap-through are suppressed. Hence the consideration of large deformations in conjunction with thermoelasticity opens many new possibilities for controlling and manipulating the thermo-mechanical response via topology optimization.

Non-dimensional process maps for residual stress in laser directed energy deposition

The nature of the residual stress and substrate melting produced by laser directed energy deposition (DED) affects the quality and reliability of the additively manufactured part. The residual stresses are induced because of temperature gradients, differences in thermal expansion coefficients and the elastoplastic behavior of the deposit / substrate material. In addition, the high cooling rate in DED can lead to additional strains, such as transformation induced plasticity and volumetric dilatation. If tensile residual stress is induced in the deposited layer, it may compromise the service life due to accelerated fatigue. The residual stress evolution depends on the process parameters and selection of right process window can yield favorable residual stresses. A validated metallo-thermomechanical finite element model for directed energy deposition is used to predict the temperature distribution and residual stress for different process conditions. The model predictions at different process conditions have been used to develop a non-dimensional empirical relationship between the residual stress and the process parameters via a nonlinear regression analysis. Isopleth of residual stress free (~0 stress) state at the deposition-substrate interface is employed to divide the process parameter subspace into two distinct domains: a detrimental tensile zone and a desirable compressive zone. It may also be noted that in order to form a sound metallurgical bond a minimal dilution (Dmin) is required which can ensure that the entire deposition melts with minimal substrate melting. Isopleth of normalized dilution of unity (D/Dmin= 1) can produce sound metallurgical bond between the deposited layer and substrate. These two isopleths in combination are crucial in identifying favorable and unfavorable domains. Such novel process maps serve as a theoretical framework in the choice of suitable process parameters to ensure the quality and integrity of the deposition.