Uniaxial Stress State Research Articles

Effect of Phase Transformation on Surface Roughening Behavior in Austenitic Thin Metal Foils

Stainless steels have wide application in the field of micro manufacturing industry. The size effect occur in thin metal foils because of low number of grain. Martensitic phase transformation (MPT) occur after plastic deformation subjected to stainless steel thin metal foils. Beside that, free surface roughening occur in thin metal foils after plastic deformation. The surface roughening mechanism in stainless steel thin metal foils after plastic deformation such as uniaxial tensile test not yet clarified well. MPT and grain misorientation (GMO) have huge effect to surface roughening behavior in stainless steel thin metal foils. The effect of GMO and MPT to surface roughening in SUS 316 and 304 thin metal foils were studied through uniaxial tensile stress state, repeated five times in 6% strain level for one time strain and 30% strain for the total of strain level. After that, an Scanning Electron Microcope-Electron Backscatter Diffraction (SEM-EBSD) analysis applied to 304 and 316 thin metal foils. The result showed that in stainless steel thin metal foil, surface roughening increase proportional both in fine gain (grain size 1,5 μm) and in coarse grain (grain size 9,0μm). The surface roughening in coarse grain, increased higher than in fine grain. The grain strength in SUS 304 is more inhomogeneous compared to SUS 316 that shown by SEM-EBSD results and as a result, increasing ratio of the surface roughness (Ra) is higher in fine grain and coarse grain of SUS 304 compared to SUS 316. The inhomogeneity of the grain strength in SUS 304 thin metal foil is higher than SUS 316 thin metal foil as shown by SEM-EBSD result. Furthermore, the increased surface roughness in stainless steel 304 is higher than stainless steel 316 thin metal foil both in fine grain and coarse grain. Key words : Surface roughening, Martensitic phase transformation (MPT), Grain Misorientation.

Fatigue fracture of steel with ferrite-martensite composite structure

The article presents results of the fatigue tests of natural steel composite material for cyclic bending in a zero loading cycle. Natural ferritemartensite composite (NFMC) has a structure of alternating layers of viscous ferrite and strong martensite, which determines special mechanism of crack deceleration under loading. Zero loading cycle presumes presence of tensile forces directed only in one side, which makes it possible to avoid work hardening of crack edges during its growth. A diagram of fatigue fracture was constructed using data obtained on kinetics of fatigue crack propagation and its growth rate, depending on the number of vibration cycles. Comparison of test results for the samples made of steel of the same chemical composition was carried out. In one case, the secondary sorbite structure ran through the traditional heat treatment. In the other, quenching of the initial row ferrite-pearlite structure in intercritical temperature range, led to obtaining ferrite-martensite composite layered structure. These materials had the same hardness, but the difference in structure organization caused the NFMC structure steel advantage in terms of resistance to fracture under cyclic loading. When crack approaches the martensite-ferrite interface, delamination occurs in ferrite due to tensile stresses parallel to the crack plane. Growth of a crack stops before additional energy is supplied for a new crack generation under conditions close to the uniaxial stress state. Method for determining characteristics of kinetics of crack growth under fatigue loading is presented and recommended for testing steels and alloys under conditions of cyclic load changes.

Dynamic properties of FeCrMnNi, a high entropy alloy

The goal of this paper was to assess the dynamic properties of a new class of materials, High entropy alloys (HEAs). Specifically, gas gun experiments coupled with recovery were performed on a specific HEA, FeCrMnNi, to measure its equation of state (EOS) and its spall strength, which is a measure of the stress required to nucleate voids under shock loading conditions. While there has been a plethora of work performed to assess the mechanical properties of these HEAs under uniaxial stress conditions as a function of strain rate, investigation of its properties in dynamic extremes remains rare. The current work fills this gap in knowledge for this novel class of materials. Our results show that the measured EOS for this material at one velocity was in reasonable agreement with an estimated Hugoniot. Furthermore, while the spall strength for this material was found to be ∼1.9 GPa, with some variation based on sample location, the main failure mode was brittle. This brittle failure leading to formation of cracks in the material is different than the ductile failure observed in pure iron and its alloys. DOE/NV/03624–1298.

ЛИНЕЙНАЯ ТЕОРИЯ УПРУГОСТИ С УЧEТОМ КВАДРАТИЧНЫХ СЛАГАЕМЫХ

We suggest a linear theory version based on Taylor decompositions for stresses and power-series for quadratic summand deformations. Thus, static equations of equilibrium in stresses are written in the form of the second-order partial derivatives differential equations. The resolving equations of equilibrium in displacements are represented in the form of the third order partial derivatives differential equations. The physical equations in this version of the linear theory of elasticity are written in the same way as in the classical linear theory of elasticity. Equilibrium equations, along with other parameters – physical constants of the medium – contain minor parameters dx, dy, dz, the value of which, as shown by numerical modelling, has little effect on the nature of the stress-strain state. It is suggested to use experimental data to determine them. Along with the formulating of the basic equations of the three-dimensional theory of elasticity, particular cases of the stress-strain state of elastic continuous medium are considered: uniaxial stressed state; uniaxial deformed state; flat deformation; generalized plane stress state. Determination of the stressed and deformed state of a thin elastic bar by integrating the resolving equations in stresses and displacements is considered as examples. The suggested version of the linear theory of elasticity, due to the quadratic summand in Taylor decompositions for stresses and in power-series for deformations, expands the classical linear theory of elasticity and, with an appropriate experimental justification, can lead to new qualitative effects in the calculation of elastic deformable bodies.

Li sublattice and diffusive response to uniaxial loads in the solid electrolyte, Li[formula omitted]La[formula omitted]Zr[formula omitted]O12 (LLZO)

The polymorphism of the garnet solid electrolyte, Li7La3Zr2O12 (LLZO), is a critical facet of the material’s performance and viability as an electrolyte candidate. Indeed, the cubic polymorph has an ionic conductivity several orders of magnitude higher than the tetragonal polymorph. While the transition from tetragonal to cubic LLZO has been reported over a range of temperatures, the response of the material to asymmetrical mechanical loads is not fully understood. To fill the knowledge gap, this paper conducted classical molecular dynamics (MD) simulations to investigate the diffusive response of LLZO under uniaxial stress conditions at 1000 K. It is found that the transition from cubic to tetragonal LLZO occurs around 500 MPa in compression and 750 MPa in tension. Near these threshold stresses, the Li sublattice undergoes a smooth transition from a cubic-like arrangement of interstitial occupancies to a tetragonal-like arrangement, with the occupancies of 24d and 96h interstitial sites decreasing and increasing respectively as the stress increases. The activation energy for diffusion increases with both tension and compression, increasing at a rate of 39 × 10−6 and 7 × 10−6 eV/MPa in compression and tension respectively.

Static and fatigue behavior of a carbon‐fiber SMC‐R composite under combined tensile and shear stresses

AbstractRandomly oriented short fiber reinforced sheet molding compound composites (SMC‐R) are among the most commonly used composites for automotive and many non‐automotive structural applications. Many studies have reported the static and fatigue properties of SMC‐R composites under uniaxial stress conditions. However, there are many applications in which they may be subjected to biaxial stress conditions and their biaxial properties have not been reported in literature. The current study considers the static and fatigue characteristics of a randomly oriented carbon fiber SMC‐R under both uniaxial and biaxial loading conditions with various combinations of tensile and shear stresses. A butterfly shaped Arcan specimen was used to conduct the biaxial stress tests. Since both static strength and fatigue life data exhibited significant variability, statistical analysis was conducted using Weibull distribution to analyse the variations in these properties of the material. In biaxial conditions in which a shear stress is imposed along with a tensile stress, the tensile strength of the material decreases with increasing shear stress. A failure envelope drawn based on von Mises equation shows reasonable agreement with the experimental results. As a percentage of the static strength, the fatigue strengths at 1 million cycles in tension and combined equal tension and shear are significantly higher than the fatigue strength in pure shear.

Mechanics of stretchy elastomer lattices

The recent advances in soft matter and advanced manufacturing have enabled the design and fabrication of elastomer lattices for versatile engineering applications. Compared with conventional engineering structures, elastomer lattices exhibit ultra-high reversible stretchability, while maintaining relatively low density. Mechanistic understanding of the mechanics of elastomer lattices is of great importance for their structural design and optimization. However, the existing studies in this field are limited to empirical models or finite element methods, while the theoretical modeling remains largely unexplored. This work reports a class of theoretical models for the mechanics of elastomer lattices over finite deformation. The potential energy function is constructed as a superposition of the stretching and bending modes, which are associated with the elongation and rotation of lattice beams, respectively. The stress-stretch behavior is determined with the aid of the principle of stationary potential energy. The model is then extended to explain the mechanics of hierarchical elastomer lattices by introducing the principal stretches in each hierarchical order as generalized coordinates. A set of holonomic constraint equations are written to define the kinematic compatibility and uniaxial stress state for hierarchical lattices, which are numerically solved via a nonlinear optimization algorithm. Results from the proposed theoretical models agree well with finite-element simulations and experiments. Case studies are performed for various material constitutive models, volume fractions, lattice architectures, and deformation modes, demonstrating the generality and robustness of the proposed theoretical models.

Examination of stress correction method of the quasi-static true stress - true strain curve considering triaxial stress state after necking initiation (2nd report)

We have proposed Analytical Iterative Uniaxial Stress Correction Method that corrects the average stress in this multiaxial state to the stress value in the uniaxial stress state by using iterative numerical simulations, and for some iron-based metals and aluminum alloys, the true stress - true strain curve in the entire strain range is obtained. In this paper, the validity of this stress correction method was verified using the design optimization / probability / statistical analysis tool LS-OPT.

Limitation analysis of the Hill48 yield model and establishment of its modified model for planar plastic anisotropy

In this paper, the limitations of the original Hill48 yield model in predicting uniaxial tensile yield stresses and r-values were analyzed in detail, and then the necessary and sufficient conditions for judging the applicability of the original Hill48 yield model were proposed. On this basis, the approximate satisfactions of the steel sheet DC04, DP980 and the aluminum alloy AA5754-O to the necessary and sufficient conditions were investigated. The results show that the necessary and sufficient conditions can be used to qualitatively analyze the predicted error of the original Hill48 model. Based on the inherent relationship of Hill48 yield function, the direction of principal stress axis was introduced into the anisotropic parameters, and a modified Hill48 model suitable for plane stress state was developed. According to the variation of the predicted error of the original Hill48 yield model in biaxial tensile stress, an exponential interpolation method including material parameter was proposed to correct the asymmetric biaxial stress between uniaxial stress state and symmetric biaxial stress state. The theoretical predicted results show that the modified model can accurately capture the directional yield stresses, r-values and yield locus. The main advantage of the modified model is that it still maintains a simple quadratic form in the stress tensor, and can significantly improve the predicted accuracy of anisotropic behavior of aluminum alloy and other materials from the use of associated flow rule.

ИССЛЕДОВАНИЕ ДИНАМИЧЕСКИХ СВОЙСТВ ДРЕВЕСИНЫ ПРИ ОДНООСНОМ СЖАТИИ

The paper presents the results of an experimental study of dynamic deformation and fracture of pine samples under compression under uniaxial stress conditions. The experiments were carried out using the classical version of the Kolsky method. Dynamic tests of pine samples cut in three directions relative to the fibers were carried out: along and across and at an angle of 45 degrees. At least three modes of loading intensity (strain rate) are implemented for each orientation of the sample. Within each mode, at least five repeated tests were carried out with the averaging of the data obtained and the determination of the scatter characteristics. As a result of the experimental study for each tested sample, time dependences of strain, stress, strain rate of the samples were obtained, deformation diagrams were constructed. The analysis of the data obtained made it possible to determine the strain rate dependences of the ultimate strains, ultimate stresses, as well as the time of the beginning of fracture (lifetime). For each direction of sample cutting, the dependences of the dynamic increase factor on the strain rate are obtained. It is shown that the strain rate significantly affects the strength and deformation characteristics of pine. A tendency to increase the ultimate values of strains and stresses with an increase in the strain rate is obtained. At the same time, the time of the beginning of fracture decreases. The influence of the loading direction of the sample relative to the orientation of the fiber was also significant. The most durable is the direction along the fiber. The dynamic increase factor for the studied directions on the right limit of the realized strain rate range was about 3. The data presented in the work can be used in the tasks of assessing the dynamic strength of structural elements made of pine.

GENERAL ANALYSIS OF STRESS AND DEFORMATION OF PARTS MOVING WITH HIGH VELOCITY IN A LIQUID OR GAS (REVIEW ARTICLE)

The article provides an analytical review and analysis of stresses and deformations of parts moving at high speeds in a liquid or gas. The working conditions of materials and parts of turbines (blades, rotor and casing) operating at high temperatures and loads are analyzed. The main ways of solving the problem of ensuring the strength of such parts are presented. The main ways to solve the problem of reliability of parts or the product as a whole are given: mathematical modeling (calculated determination of strength, durability and reliability); physical modeling (model testing); testing of full-scale products in reproducible real or operational conditions.It is impossible to speak about the strength of a part only from the calculation of deformations and stresses, even taking into account their change over time, so it is necessary to have strength criteria that establish the relationship between the strength parameters. It is emphasized that in the general case, the criterion of strength should answer the question: will the part collapse or not with the known laws of change in time of stresses, strains and temperatures It is shown that the considered standard characteristics of creep and long-term strength can be directly used in calculations only for those parts in which the uniaxial stress state at constant stresses and temperature is realized, when the working conditions of the material fully meet the test conditions of materials.An analytical view of deformation diagrams is considered as the main means of carrying out practical calculations of material strength. It is shown that in order to determine the stresses and strains in parts that move at high speeds in a liquid or gas, it is necessary to take into account the model of parts exploitation, the processes of creep and thermal fatigue of the material, and the unsteadiness of load processes. Keywords: stresses and deformations of turbine parts; deformation diagram; operating model of turbine parts; creep and thermal fatigue; nonstationarity of loading processes

INVESTIGATION OF THE OPERATING MODE OF THE DYNAMIC SYSTEM "VIBRATION PLATE - POLYMER CONCRETE" WITH SURFACE COMPACTION

For the theoretical definition of the law of motion and operating modes of the vibration plate of the surface vibration working body with polymer concrete, a study of the dynamic system "vibration plate - polymer concrete" was carried out. In this dynamic system, compacted polymer concrete is presented in the form of a system with distributed parameters, which takes into account the action of elastic and dissipative resistance forces acting on the part of polymer concrete when it is deformed into a form on a rigid foundation. According to the accepted rheological model of polymer concrete for conditions of uniaxial stress state, a partial derivative relationship is proposed between the stress and deformation of polymer concrete, the nature of which depends on the dynamic modulus of elastic deformation, the dynamic modulus of elastic deformation of Maxwell and the coefficient of dynamic viscosity. A wave equation of vibrations has been compiled, which describes the propagation of elastic-viscous deformation waves in polymer concrete, which is deformed by a surface vibrating working body, the solutions of which made it possible to determine: the regularity of propagation of elastic-viscous deformation waves in compacted polymer concrete, as well as theoretical expressions for the numerical determination of the reduced coefficients stiffness and dissipative resistance of polymer concrete, added mass; the law of motion and the amplitude of vibrations of the vibrating plate, as well as the laws of motion of the surface layer of polymer concrete. The obtained theoretical dependences make it possible to reasonably determine the rational parameters of the vibrating working body and the main operating modes of the vibrating plate, depending on the found physical and mechanical characteristics of the polymer concrete compacted by vibration. The results obtained can be further used to carry out theoretical studies on the analytical determination of the nature of the change in stresses along the height of the compacted layer of polymer concrete, as well as in the analysis and synthesis of the obtained vibro-shock mode of operation of the vibrating plate.

Accessibility of Pores to Methane in New Albany Shale Samples of Varying Maturity Determined Using SANS and USANS

The accessibility of pores to methane has been investigated in Devonian New Albany Shale Formation early-mature (Ro = 0.50%) to post-mature (Ro = 1.40%) samples. A Marcellus Shale Formation sample was included to expand the maturation range to Ro 2.50%. These are organic matter-rich rocks with total organic carbon (TOC) values of 3.4 to 14.4% and porosity values of 2.19 to 6.88%. Contrast matching small-angle neutron scattering (SANS) and ultra-small angle neutron scattering (USANS) techniques were used to generate porosity-related data before and after pressure cycling under hydrostatic (in a vacuum and at 500 bar of deuterated methane) and uniaxial stress (0 to ca. 350 bar) conditions. Our results showed that the accessible porosity was small for the samples studied, ranging from zero to 2.9%. No correlation between the accessible porosity and TOC or mineralogical composition was revealed, and the most likely explanation for porosity variation was related to the thermal transformation of organic matter and hydrocarbon generation. Pressure caused improvements in accessible porosity for most samples, except the oil window sample (Ro = 0.84%). Our data show that densification of methane occurs in nanopores, generally starting at diameters smaller than 20 nm, and that the distribution of methane density is affected by pressure cycling.

Strain-rate effect of polymers and correction methodology in a SHPB test

Split Hopkinson pressure bar (SHPB) has been commonly used to characterize the dynamic behavior of polymer at high strain-rates from 102 to 104 s−1. Based on numerical SHPB tests and Drucker-Prager model, this study examines the SHPB technique for the measurement of the dynamic strength of polymers, which is hydrostatic pressure sensitive. It is shown that the enhancement of the apparent dynamic strength above 102 s−1 strain-rate is influenced considerably by the lateral inertia confinement in the SHPB specimen. This phenomenon is accompanied by the change of the stress state (i.e., from a uniaxial stress state to a multi-axial stress state) in the SHPB specimen when the strain-rate is larger than the transition strain-rate. An iterative correction methodology is employed to identify the actual strain-rate effect. The proposed method is verified using a typical polymer of polycarbonate and can be applied to other polymers.

Hydraulic fracturing characteristics and evaluation of fracturing effectiveness under different anisotropic angles and injection rates: An experimental investigation in absence of confining pressure

Understanding and characterization of fracture propagation are crucial for enhancing the stimulation of low-permeability gas reservoirs. This study investigates the effects of shale laminate anisotropic angles (between the bedding plane and the coring orientation) and injection rates on fracture propagation in the absence of confining pressure. Results show that the variations of breakdown pressure under the uniaxial stress state are significantly different from those under conventional confining pressure: when the anisotropic angle changes from 0° to 90°, the breakdown pressure first increases and then decreases; for the increasing injection rate, there shows an apparent downward trend for the breakdown pressure. Based on macroscopic morphology descriptions, stereomicroscope imaging, and CT scanning, we show that under uniaxial stress, changing the anisotropic angle close to 45° and reducing the injection rate contribute to a more tortuous fracture path and larger stimulated fracture volume. In addition, the intersection between hydraulic fractures and bedding planes is an immediate cause of sinuous fracture morphology. Finally, three dimensionless indicators were employed to quantitatively evaluate the fracture morphology and fracturing effectiveness, which reported that the samples with low injection rate and large anisotropic angle (>45°) could achieve optimal fracturing results. The findings of this study provide important guidance for optimizing the treatment design of hydraulic fracture networks.

Hyper‐viscoelastic characterization of highly filled rubber compound: Extending approach for geometrical defect analysis

AbstractThe work provides insight into the hyper‐viscoelastic characterization of highly filled rubber compound with low structured carbon black, further examining geometrical defects using finite element (FE) simulations. The complete force‐extension behavior and stress relaxation (various strain levels [10%–100%]) in a uniaxial state of stress are reported. The extension at break is reduced by more than 42% for geometrically defective specimens. The breakage of filler–filler interaction attains equilibrium at 75% strain in stress relaxation experiment. Beyond this, the relaxation depends majorly on polymer chains. Hyperelastic material models, namely Ogden, Yeoh, and Arruda–Boyce, are chosen for the present investigation. A Prony series is used for capturing the viscoelastic properties of relaxation times. The combined utilization of the Ogden law and the Prony series in FE simulations provides an excellent match in capturing the experimental features. The effect of geometrical defects is illustrated via solving a series of numerical as well as experimental results. The simulated shape/profile changes such as necking and elliptical formation are excellently comparable with experimental results. Strain localization study shows the stress concentration zone and early prediction of failure location. The methodology presented is potentially crucial for understanding and simulating engineering rubber product's complex structures in general.

The Influence of Specimen Geometry and Loading Conditions on the Mechanical Properties of Porous Brittle Media

Dynamic tests of fine-grained fired dioxide-zirconia ceramics under compression under uniaxial stress conditions were carried out. The influence of the specimen length on the obtained strength and deformation properties of ceramics is investigated. The thickness of the specimen has a significant impact on the course of the obtained dynamic stress–strain diagrams: short specimens have a much more sloping area of active loading branch. The main contribution to the modulus of the load branch resulting from tests of brittle porous media is made by the geometry of the specimens and the porosity of the material. When choosing the length of specimens for dynamic tests, the optimal geometry of the tested specimens is preferable in accordance with the Davies–Hunter criterion, when the contributions of axial and radial inertia are mutually compensated, and the contribution of the effects of friction in the resulting diagram is minimal. When choosing the geometry of specimens of brittle porous media, the structure of the material should be taken into account so that the size of the specimen (both length and diameter) exceeds the size of the internal fractions of the material by at least five times.

Understanding asteroidal failure through quasi‐static compression testing and 3‐D digital image correlation of the Aba Panu (L3) chondrite

AbstractA comprehensive understanding of the mechanical strength and failure mechanisms of asteroids is essential for the development of hazard mitigation strategies and in situ resource extraction. In this study, the Aba Panu (L3) ordinary chondrite meteorite is investigated to understand its failure response under compressive loading. Compression experiments were conducted on ten 1 cm cubes under quasi‐static conditions in constant displacement control mode at room temperature. Three‐dimensional (3‐D) digital image correlation (DIC) was used to measure the full‐field deformation and strain. These data were used to determine the elastic modulus and local strain distribution, and investigate the effects of the mineralogical and structural heterogeneity on the crack formation and growth sites. Aba Panu exhibits brittle failure during compression with a range of failure strength from 361.7 to 578.0 MPa. Axial splitting and multiple fracturing occur during the uniaxial compressive state of stress. Ultrasonic tests were used to calculate elastic moduli from sound speeds and compared with the results of L‐type ordinary chondrites from the literature. Characterization results from electron microprobe analysis identified different elements and areal distribution of mineral phases and pre‐existing cracks. In general, the DIC results did not show correlations between crack initiation and specific mineralogical or textural components in this meteorite, such as chondrules or metals/sulfide grains, suggesting that the pre‐existing microcracks and porosity control the Aba Panu failure mechanisms.

Biaxial residual stress measurement by indentation energy difference method: Theoretical and experimental study

In this paper, an energy difference method is proposed to estimate biaxial stress components based on indentation technique. The indentation energy is chosen as an analytical parameter, which can be calculated directly from the load-depth curve. The presence of residual stress in a material causes the change of indentation energy. The mapping relationship between uniaxial stress and indentation energy difference was established by finite element analysis. Meanwhile, the Knoop tip was applied since the indentation response varies according to the indenter orientation. Using this feature, a biaxial stress state can be transformed into two equivalent uniaxial stress states by indentation energy conversion. Finally, the biaxial residual stress components can be solved by the energy difference functions of two orthogonal indentations. A portable indentation instrument was developed to implement this approach, which is suitable for in-site measurement. The obtained results show good agreements with the artificial stresses applied by cross-shape sample experiment.

Fatigue life analysis of carbon fiber reinforced polymer (CFRP) components in hybrid adhesive joints

AbstractHybrid adhesive joints of metal and composite parts are increasingly common features of lightweight structures. Efficient design of these joints requires computational methods for estimating the fatigue life of the adhesive as well as of the parts being joined – i. e. the adherends. The paper focuses on computational fatigue life prediction for carbon fiber reinforced polymer (CFRP) adherends in hybrid adhesive joints. After a brief description of the composite material considered, two modeling approaches for the fatigue life are presented. Subsequently, the experimental determination of the model parameters is discussed and the relevant values are presented. For validation, the models are applied to predict the fatigue lives of a multidirectional laminate as well as of the composite adherend in a hybrid single‐lap joint. Finally, the results for both models are compared and discussed with respect to the experimental results. Both models yield reasonable predictions for the cases considered here. For almost uniaxial stress states, the predictions of both models are very similar while for multiaxial stress states the difference is more pronounced.