Multiaxial Stress Research Articles

Nucleation under multi-axial loading in variational phase-field models of brittle fracture

Phase-field models of brittle fracture can be regarded as gradient damage models including an intrinsic internal length. This length determines the stability threshold of solutions with homogeneous damage and thus the strength of the material, and is often tuned to retrieve the experimental strength in uniaxial tensile tests. In this paper, we focus on multiaxial stress states and show that the available energy decompositions, introduced to avoid crack interpenetration and to allow for unsymmetric fracture behavior in tension and compression, lead to multiaxial strength surfaces of different but fixed shapes. Thus, once the length scale is tailored to recover the experimental tensile strength, it is not possible to match the experimental compressive or shear strength. We propose a new energy decomposition that enables the straightforward calibration of a multi-axial failure surface of the Drucker-Prager type. The new decomposition, which hinges upon the theory of structured deformations, encompasses the volumetric-deviatoric and the no-tension models as special cases. Preserving the variational structure of the model, it includes an additional free parameter that can be calibrated based on the experimental ratio of the compressive to the tensile strength (or, if possible, of the shear to the tensile strength), as successfully demonstrated on two data sets taken from the literature.

Hydrogen diffusivity and solubility in stressed fcc crystals

Although many materials are used under extreme conditions, the effects of stress and strain are often neglected in material studies, especially when studying the solubility or calculating the diffusivity of substitutional or interstitial species. In this work, a general method based on first-principles calculations and elasticity theory in fcc systems is presented to fill this gap. The case of hydrogen in aluminum is investigated in detail as an application sample by comparing results from the density functional theory (DFT) and the elasticity theory. Additional systems, Ni, Cu and Pd, are also examined for hydrogen but in the framework of the elasticity theory only. Different types of stresses, i.e. hydrostatic, multi-axial and shear stress, are investigated for comparison purposes. The symmetry break induced by the loading is analyzed at the atomic scale by calculating the jump rates, at macroscopic scale from computed diffusion coefficients. Equations of diffusion are developed for each loading. Results show that the effect of loading on atomic parameters – insertion energies, energy barriers, etc.– can be accurately captured by the elasticity theory in terms of elementary parameters calculated using the DFT. Results show that the effect of stress is weak in the case of hydrogen.

Temperature-dependent deformation behavior of γ and γ′ single-phase nickel-based superalloys

High-temperature nanoindentation measurements were employed to reveal the fundamental deformation behavior of γ and γ′ single-phase in nickel-based superalloy at various temperatures. The single-crystal samples of each phase with the equilibrium chemical compositions as in the conventionally utilized alloy were used to elucidate the temperature-dependent behavior of the individual phase leading to a further interpretation of each phase effect in the intensively used dual-phase alloy. Nanoindentation tests were conducted at room and elevated temperatures on the γ and γ′ single-phase using the Berkovich diamond indenter probe, and the Hysitron's xSol800 high-temperature stage. The noiseless load-displacement curves were obtained owing to thermal stability up to 1073 K and 873 K on the γ and γ′ sample, respectively. Furthermore, load-displacement curve shows a clear plasticity initiation in a strain burst as “pop-in” on a loading segment. The number of pop-in events in load-displacement curves of both, the γ and γ′ samples, increases with temperature. The elastic modulus and hardness of the γ phase decrease as the temperature increases, while the γ′ phase demonstrates thermal stability up to 573 K, indicating the γ′ phase domination for the high-temperature property in the dual-phase alloy. At small-scale mechanical property measurements no inverse temperature dependence of hardness was detected for the γ′ phase as a consequence of the multi-axial stress state with high hydrostatic pressure. Further, real-time topographical observations of the surface with increasing temperature reflect the behaviors of slip deformation and oxidation evolution.

Local stress based fatigue assessment of multiaxially stressed automotive antiroll bars

Using a high-strength, cold formed and shot peened antiroll bar for heavy duty truck axles subject to multiaxial-proportional bending and torsion as an example, the paper shows a stress based fatigue life assessment procedure applicable in the early design phase of such high-performance suspension components with pronounced surface treatment. Finite element simulations reveal the component’s failure-critical locations and the multiaxial stress state acting there under the applied operational load. Strain gage measurements on prototype antiroll bars verifiy the accuracy of the simulations. Theoretical design S-N curves have been derived using the FKM-guideline recomendations regarding the material fatigue properties and correction factors accouting for the surface treatment (shot peening), in conjunction with the FEM results. The paper gives insight and explains the theoretical approach to local stress-based multiaxial fatigue analysis. Fatigue tests under fully reversed costant amplitude loading verify the theoretically determined S-N curves. The good agreement betrween experimental and theoretical fatigue lives pinpoints the great potential of the stress-based procedure described within the FKM guideline for treating multiaxial-proportional loading and life influencing effects resulting from the surface treatment in full-scale industrial components.

Crack growth models for multiaxial fatigue in a ship’s propeller shaft

A premature fatigue failure of a large intermediate propeller shaft in a shuttle tanker is discussed and analyzed. The short fatigue life consists mainly of a crack growth phase. Life predictions are carried out by crack growth modelling based on engineering fracture mechanics. The purpose of the present investigation is to identify the most likely loading modes based on the evolution of the crack propagation. A Linear Elastic Fracture Mechanics Model (LEFM) is applied with the stress intensity factor range entering the Paris law as a key parameter. Existing formulas for the geometry functions are supplemented by more detailed stress intensity factor calculations pertaining to small semi-elliptical surface cracks subjected to stress mode I. Enhanced geometry functions are proposed as a function of the relative crack depth and the crack shape aspect ratio. The ability of the fracture mechanics model to reconstruct the observed crack path and crack shape development is emphasized. Various loading modes and multi-axial stress states are applied to pursue the observed crack behavior. The observed semi-elliptical crack shapes and the shift in crack planes are included in the analysis.

Analytical modelling of continuous fibre-reinforced thermoplastics’ thermomechanical properties and implementation into a failure model

Mechanical properties of fibre-reinforced thermoplastics show a remarkable temperature dependence within application temperatures of automotive and aerospace lightweight structures. To take this dependence into account when designing components, the strengths (, , , , ) and stiffnesses (, , , , ) of continuous carbon and glass fibre-reinforced polyamide 6 and glass fibre-reinforced polypropylene are modelled analytically based on experiments. Data from temperature-controlled tests on flat samples in the range from -20 °C to +80 °C are therefore approximated using an extended hyperbolic approach. The models obtained are then evaluated based on their deviation from the experimental values. The main criterion of this evaluation is the reliable prediction of the temperature-dependent material properties while minimising the effort for generating test data and determining model parameters. Furthermore, the failure behaviour of the investigated materials under multiaxial mechanical and thermal stress is examined by implementing the determined strength curves into Cuntze’s physically based failure criterion.

RESEARCH ON THE CREEP OF CONCRETE FILLED STEEL TUBULAR COLUMNS BASED ON THE GENERALIZED KELVIN CHAIN

Concrete creep is an inherent time-dependent behavior of concrete and an important composition of structural responses. Its calculating method is usually established on the basis of uniaxial test and theory. To explore the creep behavior of concrete-filled steel tubular columns, the creep of circular concrete columns and concrete filled circular steel tubular (CFST) columns were measured by a self-made and self-balanced loading device. The results show that the creep deformation of CFST columns is smaller than that of concrete columns. In the present concrete creep tests, the maximum difference between the two aforementioned creep deformations was close to 50%. It is attributed to the fact that the core concrete cannot exchange moisture with its external atmosphere environment so that no dry shrinkage and creep of the core concrete occurred. It is also attributed to the confining pressure of the steel tube. According to the theory of viscoelasticity, a Volterra integral equation for solving the concrete creep under uniaxial stress condition was established by introducing a model consisting of a multi-parameter Kelvin element chain. The model parameters were approximately expressed as a successive retardation spectrum. Therefore, the constitutive relationship of concrete creep stress and strain increments under uniaxial stress condition was derived by discretizing the time variable t and integration by parts. Based on the principle of creep superposition and the Poisson effects, the constitutive model of the concrete creep stress and strain increments under uniaxial stress condition state was extended to a multiaxial stress state to analyze the CFST creep. The commercial finite element analysis software Ansys was secondarily-developed. The constitutive equation under multiaxial stress state for concrete creep performance was compiled with the Fortran language and introduced into the user subroutine Usermat of Ansys. Finally, the finite element numerical analysis for the long-term creep performance of CFST columns was carried out. Comparing the numerical solutions with the test results, it is found that the proposed method provides another effective approach to the analysis of concrete creep.

Magnetization Reversals of Fe81Ga19 -Based Flexible Thin Films Under Multiaxial Mechanical Stress

The effect of multiaxial mechanical stress on angle-dependent magnetization reversals is studied on a single 10-nm ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ film, a single 10-nm ${\mathrm{Fe}}_{81}{\mathrm{Ga}}_{19}$ film, and a ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(10 nm)/${\mathrm{Fe}}_{81}{\mathrm{Ga}}_{19}$(10 nm) bilayer. These films are grown on flexible $\mathrm{Al}$ ``kitchenlike'' foils. These flexible foils are bent on two convex optical lenses to apply multiaxial mechanical stresses of different magnitudes. In order to understand the mechanisms driving the physical properties of the flexible systems, the magnetic films are also grown on hard native-oxide-covered $\mathrm{Si}$(100) substrates. By probing the angular dependence of the coercive field and the remanent magnetization, we show that the ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ single layer and the ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}/{\mathrm{Fe}}_{81}{\mathrm{Ga}}_{19}$ bilayer grown on $\mathrm{Si}$ present a uniaxial anisotropy. Along their easy axis, their domain structure at the coercive field exhibits large domains with sawtooth domain walls. However, the ${\mathrm{Fe}}_{81}{\mathrm{Ga}}_{19}$ layer grown on $\mathrm{Si}$ shows a cubic anisotropy and sharp domain walls with a right-angle geometry along its easy axis. All layers grown on $\mathrm{Al}$ foils show development or enhancement of a uniaxial anisotropy arising from the $\mathrm{Al}$ surface morphology. Multiaxial mechanical stress applied to the flexible $\mathrm{Al}$ foils results in very different nonreversible effects as a function of the composition of the layered system. For ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$, multiaxial mechanical stress has no effect, as expected for a nonmagnetostrictive system. For ${\mathrm{Fe}}_{81}{\mathrm{Ga}}_{19}$, it results in a full in-plane randomization of its magnetization-reversal properties. For the bilayer, multiaxial mechanical stress does not fully randomize the in-plane magnetization-reversal properties: the bilayer retains a uniaxial character.

Temperature dependence of viscoelastic Poisson\u2019s ratio of cement mortar

Concrete creep research has focused primarily on uniaxial response. However, biaxially prestressed concrete structures are common, resulting in a multiaxial stress state that can complicate the behavior of a viscoelastic material like concrete. Significant creep strains may be induced in directions transverse to each principle stress due to Poisson’s effect. Past research is unclear regarding the viscoelastic or viscoplastic properties of concrete outside of uniaxial response. It has been reported in separate studies that concrete viscoelastic/viscoplastic Poisson’s ratio (VPR) is an increasing, decreasing and constant function with time, with all reported measurements performed at room temperature. In this paper, the 3D basic creep response of mature cement mortar is examined using a confined compression experiment that allows direct determination of the full stress and infinitesimal strain tensors in a single test, which enables the determination of VPR under a multiaxial stress state. For this purpose, a unique, miniature version of the standardized concrete creep frame is designed that is amenable to placing in climate chambers and temperature ovens. The experimental results indicate that the VPR of sealed, mature cement mortar is nearly constant and equal to the elastic at room temperature, while the VPR gradually increases with time when measured at 60 °C.

Stress states investigation of adhesive bonded joint between spar cap and shear webs of a large wind turbine rotor blade

The debonding failure at the adhesive bonded joints between spar caps and shear webs is one of failure modes of the wind turbine rotor blades. To avoid such a failure, the numerical investigation of stress states at the adhesive bonded joints is important to assess the structural integrity of a rotor blade subjected to the extreme bending moments. In this paper, the simplified stress state calculation method was derived based on the multiaxial stress states of shear webs computed from the linear elastic composite analysis from ANSYS 19.2. From the close investigation of a small blade and a large blade, it turned out that the care must be taken evaluating stresses of a large blade with double shear webs than a small one with a single web. In case of a large blade, the adhesive structure between spar cap and a shear web close to an aft shear web (ASW) showed higher stresses compared to the adhesive part located to a forward shear web (FSW). Especially, the out-of-plane stresses of the adhesive at ASW were increased toward the outboard region of a blade, while the stress level of the adhesive at FSW was almost constant along the blade length, which is similar to a single shear web case of a small blade (< 25 m). It indicates the higher peeling failure possibility at the interface between the adhesive and an ASW when blade size is increased.

Discontinuous plastic flow in stainless steels subjected to combined loads at extremely low temperatures

In the present paper, the question of the mechanism of discontinuous plastic flow (DPF) occurring at extremely low temperatures (in the proximity of absolute zero), is for the first time raised in the context of kinematically controlled combined loads (independent control of displacement and rotation) and non-proportional loading paths. In order to identify the multiaxial stress state during DPF, a unique set-up for testing tubular samples under kinematically controlled traction and torsion in liquid helium (4.2 K) has been developed. The results of tests performed on grade 304 stainless steel thin-walled tubular samples subjected to combined loads (traction and torsion) in the proximity of absolute zero are for the first time reported. These novel results confirm the assumptions accepted when building the multiaxial constitutive model of discontinuous plastic flow, namely, the production of lattice barriers, the pile-ups of dislocations and the criterion of their collective failure, as well as the assumption that the serrations may be recorded by force and torque transducers independently. Thus, the numerically implemented model allows to reproduce the observed serrations, and to redistribute them between the loading directions.

A micromechanical model of carbon fiber-reinforced plastic and steel hybrid laminate composites

The fracture strain of carbon fiber-reinforced plastics (CFRPs) within CFRP/steel hybrid laminate composites is reportedly higher than that of CFRPs due to transverse compressive stress induced by the steel lamina. A micromechanical model was developed to explain this phenomenon and also to predict the mechanical behavior of CFRP/steel hybrid laminate composites. First, the shear lag theory was extended to calculate stress distributions on fibers and matrix material in a CFRP under multiaxial stress condition, considering three deformation states of matrix (elastic and plastic deformation and fracture) and the transverse compressive stress. Then, the deformation behavior of CFRP was predicted using average stress in the ineffective region and the Weibull distribution of carbon fibers. Finally, the mechanical properties of CFRP/steel hybrid laminate composites were predicted by considering the thermal residual stress generated during the manufacturing process. The micromechanical model revealed that increased transverse compressive stress decreases the ineffective lengths of partially broken fibers in the CFRP and results in increased fracture strain of the CFRP, demonstrating the validity of the current micromechanical model.

Multiscale constitutive model using data–driven yield function

To overcome inaccurate prediction of yield surface evolution arising from the general use of classical yield functions, a method to formulate data-driven yield functions is established, using machine learning technique operating on the multi-axial yield data that exhibit the unique multi-axial hardening behavior of amorphous polymers. A scheme to generate sufficient data for multi-axial hardening responses is proposed, using molecular dynamics simulations, considering their timescale limitations, on quantitative estimations of mechanical responses. Based on the mined data-driven yield function, a constitutive model is constructed, and the corresponding multi-axial stress evolutions are compared with those of classical models. To examine the possibility of yield function mining by symbolic regression, the development of the classical yield functions von–Mises, Drucker–Prager, Tresca, Mohr–Coulomb, and paraboloidal yield functions was reproduced by using the proposed approach. Additional simulations were undertaken to characterize the influence of noise in the yield data set on the chosen functions.

Determination of Plastic Material Properties of Thin Metal Sheets under Electromagnetic Forming Conditions

Electromagnetic forming is a contactless high-speed forming technique. In this process force transmission is initiated by an electromagnetic field provided by a tool coil. While forming thin sheet metal, the magnetic field is present in the whole depth of the sheet metal by definition. Thus, the magnetic field generates eddy currents in the complete sheet volume. The resulting Lorenz` forces act as body forces and are used for forming. Thereby high strain rates, high temperatures and multiaxial stress fields influence the plastic material properties of the workpiece. In this study, the plastic properties were investigated under real electromagnetic forming conditions. By varying process conditions like charge energy, sheet thickness and die material, the magnetic field and thus the plastic material properties were changed. To visualize the influence of the electromagnetic field, forming experiments were carried out. The strain of the formed sheets was measured. Furthermore, the forming forces were determined by measurements during the electromagnetic forming as well as by finite element simulations. With the measured strain and the determined forming force, a model for the plastic material behavior during electromagnetic forming was evolved.

Defect‐based multiaxial fatigue life prediction of L‐PBF additive manufactured metals

AbstractFatigue cracks in additively manufactured (AM) components typically initiate from critical defects such as gas porosities and lack of fusion defects. In addition, such components are often subjected to multiaxial stresses at fatigue critical locations due to complex geometry and/or multiaxial loads. In this work, a fracture mechanics framework based on defects and their characteristics was used for multiaxial fatigue life prediction of laser‐based powder bed fusion (L‐PBF) fabricated Ti‐6Al‐4V and 17‐4 PH specimens as illustrative examples. Modes I and II and mixed‐mode small crack growth were considered in the predictions based on the experimentally observed damage mechanisms, depending on the metal, fabrication process, and post‐process treatment conditions. Implications of initial defects characteristics under multiaxial loading and the effect of roughness‐induced closure in mixed‐mode crack growth are also discussed.

Analytical models of the strength and ductility of CNT reinforced metal matrix nano composites under elevated temperatures

Carbon nanotubes (CNTs) can greatly enhance the strength of metal matrix composites while resulting in ductility loss. This strength-ductility tradeoff dilemma always confines the development of material design and real-life applications. In this work, a temperature dependent strengthening analytical model is proposed for CNT reinforced metal matrix composites which considers three common strengthening mechanisms: Orowan looping effect, thermal expansion mismatch effect, and load bearing effect. The proposed model can predict composite material strength with different volume fractions of CNTs and under different temperatures. Combining the strengthening model with the stress based modified Mohr-Coulomb (sMMC) ductile fracture model, a ductility analytical model is then derived. This ductility analytical model includes the influences of temperature, multi-axial stress loading conditions, as well as the aforementioned three strengthening mechanisms. A good agreement has been achieved between literature published experimental data and analytical predictions for both composite material strength and ductility loss. The proposed two analytical models can provide a straightforward way to study the strength-ductility relationship for CNT reinforced metal matrix composites over a wide range of temperatures and different stress states, and then provide guidance on new material design and processing.

Multiaxial fatigue assessment of complex steel connections: A case study of a vertical-lift gussetless truss bridge

Civil engineering structures grow more complex as engineers push innovation boundaries. Load complexity, costs, construction and maintenance efficiency, among other things, can lead to unique designs that are often excluded in current design codes and evaluation standards. Fatigue-induced damage is currently one of the most common damage types experienced by ordinary and complex civil engineering structures subjected to cyclic loading such as bridges. However, current fatigue evaluation and design standards provide limited guidance on how to approach complex welded connections. Uniaxial and multiaxial methods for the evaluation of fatigue life using strains histories are compared for the assessment of a welded gussetless truss connection of the Memorial Bridge, a vertical-lift bridge connecting Portsmouth, NH and Kittery, ME. As expected, using both approaches result in sufficient remaining fatigue life. However, it is demonstrated that commonly used uniaxial fatigue analysis methods can be insufficient in complex structures that experience variable amplitude, multiaxial, and non-proportional loading. Multiaxial non-proportional stresses experienced by a complex connection can cause a decrease in remaining fatigue life estimates. This paper presents assessment tools and a method for the evaluation of fatigue life of complex welded connections using strain time histories.

Thermo-cycling fatigue of SiMo ductile iron using a modified thermo-mechanical test

Cast exhaust manifolds are made from silicon and molybdenum (SiMo) alloyed ductile iron. These complex-shaped, thin-walled cast components are subjected to heating and cooling cycles during service under mechanically constrained conditions. This type of load condition can induce multiaxial stress that can promote thermo-mechanical fatigue (TMF). In addition, high temperature oxidation in combination with thermo-mechanical load can accelerate degradation of the thin wall cast component during extended service. In this article, a modified mechanically constrained thermal cycling test, which generates transient multi-axial stress, is presented. Finite Element Modeling (FEM) was performed to design a specimen geometry and simulate the stresses and deformation during sequential thermal cycles. The test system uses a heating unit that passes direct current through the sample (Joule heating) and monitors the loads generated by thermal expansion of the specimen. The measured loading profile during thermal cycling was similar to the profiles obtained from FEM simulations. Several tests were performed using SiMo ductile iron with multiple thermal cycle profiles to verify the effect of temperature and oxidation time on TMF fatigue. In addition, thermal diffusivity, differential scanning calorimetry, dilatometry, and oxidation tests were performed to analyze high temperature properties of SiMo cast iron in quasi-static condition. High resolution microscopy was used to analyze the thermo-cycled specimens and it was found that the oxidation and decarburization can significantly affect the resistance of SiMo ductile iron crack formation during thermal cycling. The suggested test method permits the use of a small test specimen directly extracted from a thin-walled casting with the original cast structure and can be used for verification of critical service temperature, alloy design, and ductile iron process optimization.

An improved methodology of constructing inter-fiber failure criteria for unidirectional fiber-reinforced composites

Based on Mohr’s failure theory and physical mechanisms of unidirectional (UD) fiber-reinforced composites, an improved methodology of constructing inter-fiber failure (IFF) criteria is proposed. The expression of the failure criteria is a quadratic polynomial, in which the variables are the normal and shear stress components (σn,τnl,τnt) on the potential failure plane. The coefficients of the quadratic polynomial are independent of empirical parameters and calibrated only by four basic strengths of a UD composite, i.e. transverse tensile and compressive strengths, Yt and Yc, as well as transverse and longitudinal shear strengths, S23 and S21. It avoids some deficiencies of the previous criteria for IFF in which some parameters may need to be determined by multiaxial stress tests or by empirical data-fitting operation. Compared with the theoretical prediction results and the experimental data of various UD composites, the present IFF criteria show good prediction accuracy.

Extension of the static equivalent stress hypotheses to linearly vibrating systems using wave interference – The LiWi approach

This paper presents a damage-equivalent stress, to be related to uniaxial S-N curves for mechanical systems undergoing multiaxial stress cycles for evaluating fatigue strength. It covers variable and non-proportional loads, wherein the known static equivalent-stresses from von-Mises, Tresca and Rankine are extended to oscillating systems using wave interference. This novel approach is termed as LiWI (Linear Wave Interference) and leads to physically valid signal progressions, allowing for frequency content preservation, rotational invariance and application to static cases. Hence a unification of the equivalent stress descriptions in time, frequency and stochastic (power spectral density) domains for linear time invariant systems results.