Cyclic Stress-strain Curve Research Articles

An Investigation and Prediction of Springback of Sheet Metals under Cold Forming Condition

Low formability and springback especially at room temperature are known to be major obstacles to advancements in sheet metal forming industries. The integration of numerical simulation within the R&D activities of the automotive industries provides a significant development in overcoming these drawbacks. The aim of the present work is to model and predict the springback of a Galvanized low carbon steel automotive panel part. This part suffers from both positive and negative springback which physically measured using CMM. The objective is to determine the suitable forming process parameters that minimize and compensate the springback through robust FE model. The analysis of the springback was carried out following (Isotropic model and Yoshida – Uemori model) which are calibrated through cyclic stress strain curve. The material data of the Galvanized low carbon steel was implemented via lookup tables in the commercial finite element software Pam-Stamp(TM). Firstly, the FE model was validated using the deformed part which suffers from springback problem at the same forming condition. The FE results were compared with the measured experimental trails providing very good agreement. Secondly, the validated FE model was used to determine the suitable forming parameters which could minimise the springback of the deformed part.

Fracture-mechanics based prediction of the fatigue strength of weldments. Material aspects

Any fracture mechanics based determination of the fatigue strength of weldments requires different input information such as the local weld geometry and material data of the areas the crack is passing through during its propagation. The latter is so far not a trivial task as the fatigue crack is usually initiated at the weld toe at the transition from the weld metal to the heat affected zone. Furthermore, the crack propagates through the different microstructures of the weldment even into the base metal and causes final fracture. This paper describes how the material input information has been gained particularly for heat affected zone material by thermo-mechanically simulated material specimens for two steels of quite different static strength. The data comprise the cyclic stress-strain curve, the crack closure effect-corrected crack growth characteristics, fatigue threshold values for long cracks, the dependency of the parameter on the crack length and monotonic fracture resistance. The substantial experimental effort was necessary for the validation exercises of the IBESS approach, however, within the scope of practical application more easily applicable estimating methods are required. For that purpose, the paper provides a number of appropriate proposals in line with its check against the reference data from the elaborate analyses.

Ferroelasticity in an Organic Crystal: A Macroscopic and Molecular Level Study

AbstractFerroelasticity has been relatively well‐studied in mechanically robust inorganic atomic solids but poorly investigated in organic crystals, which are typically inherently fragile. The absence of precise methods for the mechanical analysis of small crystals has, no doubt, impeded research on organic ferroelasticity. The first example of ferroelasticity in an organic molecular crystal of 5‐chloro‐2‐nitroaniline is presented, with thorough characterization by macro‐ and microscopic methods. The observed cyclic stress–strain curve satisfies the requirements of ferroelasticity. Single‐crystal X‐ray structure analysis provides insight into lattice correspondence at the twining interface, which enables substantial crystal bending by a large molecular orientational shift. This deformation represents the highest maximum strain (115.9 %) among reported twinning materials, and the associated dissipated energy density of 216 kJ m−3 is relatively large, which suggests that this material is potentially useful as a mechanical damping agent.

Ferroelasticity in an Organic Crystal: A Macroscopic and Molecular Level Study.

Ferroelasticity has been relatively well-studied in mechanically robust inorganic atomic solids but poorly investigated in organic crystals, which are typically inherently fragile. The absence of precise methods for the mechanical analysis of small crystals has, no doubt, impeded research on organic ferroelasticity. The first example of ferroelasticity in an organic molecular crystal of 5-chloro-2-nitroaniline is presented, with thorough characterization by macro- and microscopic methods. The observed cyclic stress-strain curve satisfies the requirements of ferroelasticity. Single-crystal X-ray structure analysis provides insight into lattice correspondence at the twining interface, which enables substantial crystal bending by a large molecular orientational shift. This deformation represents the highest maximum strain (115.9 %) among reported twinning materials, and the associated dissipated energy density of 216 kJ m-3 is relatively large, which suggests that this material is potentially useful as a mechanical damping agent.

Plieno ciklinio nestabilumo įvertinimas esant mažacikliam deformavimui

Šiame straipsnyje, apdorojus 286 medžiagų standaus apkrovimo tyrimo rezultatus, mėginta įvertinti medžiagų ciklinių savybių sritis pagal mechanines charakteristikas. Tyrimas parodė, kad pagal santykį Rm / ReL ir (Rm / ReL)Z, taip pat koordinatėse Rm / ReL – Z cikliškai stabilios medžiagos yra tuose pačiuose intervaluose kaip ir cikliškai nestabilios (silpnėjančios, stiprėjančios) medžiagos, todėl jų skirstymas pagal ciklines savybes nepavyko. Nuodugniai rezultatų analizei atlikti buvo pasirinktas mažaciklio apkrovimo kreivių parametras a, kuris tiksliausiai apibūdina medžiagos stiprėjimo (silpnėjimo) intensyvumą.

Dynamic characteristics of expanded polystyrene composite soil under traffic loadings considering initial consolidation state

As a type of artificial filling material, the shear modulus and damping ratio of expanded polystyrene (EPS) composite soil are two key parameters used to analyze the dynamic stability of an embankment. Nineteen combined axial–torsional tests are conducted on hollow cylinder specimens of EPS composite soil to study its dynamic characteristics under the complex stress path induced by the simulated traffic loadings. The characteristics of skeleton curve, dynamic shear modulus and damping ratio for EPS composite soil are analyzed. It is found that EPS composite soil is characterized by typical dynamic nonlinearity, which is influenced by the mixing ratio and the initial stress state. The increasing cement content can effectively improve the dynamic strength of EPS composite soil. EPS bead content has a slight influence on the initial shear modulus of EPS composite soil as well as the cyclic stress-strain curve in the linear elastic stage. However, the increasing EPS bead content obviously reduces the dynamic strength. The initial shear modulus increases with increasing initial minor principal stress for the isotropic and anisotropic consolidated specimens. The characteristics of modulus attenuation are significantly influenced by the initial minor principal stress, EPS bead content and initial rotation angle of the major principal stress axis. The “structural damping” effect induced by the weak interface formed between EPS beads and cemented soil is an important component of the damping mechanism for the EPS composite soil. Based on the experimental results, this paper provides the empirical models to describe the skeleton curve, modulus attenuation and damping growth characteristics for EPS composite soil.

Effect of contact pressure on multiaxial fretting fatigue behavior of Al-Zn-Mg alloy

Abstract This research investigates effects of contact pressure on multiaxial fretting fatigue behavior of Al-Zn-Mg alloy which has a wide variety of applications in automobile and rail transit engineering. Al-Zn-Mg alloy is exposed to cyclic loadings and contact pressure. The cyclic stress-strain curve and displacement amplitude curve under different contact pressure of Al-Zn-Mg alloy were investigated using point contact multiaxial fretting fatigue test equipment. Based on cyclic stress-strain curve and displacement amplitude curve under different contact pressure, fretting wear characteristics, fretting fatigue fracture properties and fretting fatigue lives as well as the effects of contact pressure on multiaxial fretting fatigue damage and fretting fatigue fracture mechanisms of Al-Zn-Mg alloy were extensively analyzed.

Stress softening and hardening during compression and tensile consecutive cyclic loading of Mn18Cr18N austenitic stainless steel

The compression and tensile consecutive deformation behavior and microstructure evolution of Mn18Cr18N steel were investigated by cyclic loading tests at room temperature and strain amplitude from 0.005 to 0.15. The results indicated that the cyclic loading stress-strain curves of the steel show plastic deformation characterized by almost the same working hardening rates without yield plateaus at various strain amplitudes. At the lower strain amplitudes from 0.005 to 0.01, the stress amplitudes and subsequent yield surface radius decreased with cycles, which suggest that stress softening occurs during cyclic loading. At the strain amplitudes from 0.02 to 0.15, the stress amplitudes and subsequent yield surface radius increased with cycles, which imply that stress hardening occurs during cyclic loading. With the increasing of strain amplitudes, the cyclic hardening coefficients monotonically increased, while the cyclic softening coefficients rapidly decreased. The maximum flow stress increased up to 1549.6MPa after three cycles at the strain amplitude of 0.15, which increased by 395.4MPa compared to the maximum uniaxial tensile flow stress. It was also demonstrated that the cyclic loading stress-strain behaviors (cyclic softening and hardening) depend on internal stress component rather than effective stress component. TEM observation shows that planar slip with parallel substructures along one direction at high number cycles evolved from various dislocation configurations at low number cycles occurs at the lower strain amplitude of 0.005; double planar slip with grid substructures along two directions at high number cycles evolved from parallel substructures along one direction at low number cycles occurs at the higher strain amplitude of 0.04. Internal stress could be released by dislocation rearrangement and activation of cross slips during cyclic loading process, which induce stress softening at lower strain amplitudes; while slipping and twining alone two intersectional directions caused stress hardening at higher strain amplitudes.

On cyclic yield strength in definition of limits for characterisation of fatigue and creep behaviour

AbstractThis study proposes cyclic yield strength as a potential characteristic of safe design for structures operating under fatigue and creep conditions. Cyclic yield strength is defined on a cyclic stress-strain curve, while monotonic yield strength is defined on a monotonic curve. Both values of strengths are identified using a two-step procedure of the experimental stress-strain curves fitting with application of Ramberg-Osgood and Chaboche material models. A typical S-N curve in stress-life approach for fatigue analysis has a distinctive minimum stress lower bound, the fatigue endurance limit. Comparison of cyclic strength and fatigue limit reveals that they are approximately equal. Thus, safe fatigue design is guaranteed in the purely elastic domain defined by the cyclic yielding. A typical long-term strength curve in time-to-failure approach for creep analysis has two inflections corresponding to the cyclic and monotonic strengths. These inflections separate three domains on the long-term strength curve, which are characterised by different creep fracture modes and creep deformation mechanisms. Therefore, safe creep design is guaranteed in the linear creep domain with brittle failure mode defined by the cyclic yielding. These assumptions are confirmed using three structural steels for normal and high-temperature applications. The advantage of using cyclic yield strength for characterisation of fatigue and creep strength is a relatively quick experimental identification. The total duration of cyclic tests for a cyclic stress-strain curve identification is much less than the typical durations of fatigue and creep rupture tests at the stress levels around the cyclic yield strength.

A Fatigue Life Prediction Method Based on Strain Intensity Factor.

In this paper, a strain-intensity-factor-based method is proposed to calculate the fatigue crack growth under the fully reversed loading condition. A theoretical analysis is conducted in detail to demonstrate that the strain intensity factor is likely to be a better driving parameter correlated with the fatigue crack growth rate than the stress intensity factor (SIF), especially for some metallic materials (such as 316 austenitic stainless steel) in the low cycle fatigue region with negative stress ratios R (typically R = −1). For fully reversed cyclic loading, the constitutive relation between stress and strain should follow the cyclic stress-strain curve rather than the monotonic one (it is a nonlinear function even within the elastic region). Based on that, a transformation algorithm between the SIF and the strain intensity factor is developed, and the fatigue crack growth rate testing data of 316 austenitic stainless steel and AZ31 magnesium alloy are employed to validate the proposed model. It is clearly observed that the scatter band width of crack growth rate vs. strain intensity factor is narrower than that vs. the SIF for different load ranges (which indicates that the strain intensity factor is a better parameter than the stress intensity factor under the fully reversed load condition). It is also shown that the crack growth rate is not uniquely determined by the SIF range even under the same R, but is also influenced by the maximum loading. Additionally, the fatigue life data (strain-life curve) of smooth cylindrical specimens are also used for further comparison, where a modified Paris equation and the equivalent initial flaw size (EIFS) are involved. The results of the proposed method have a better agreement with the experimental data compared to the stress intensity factor based method. Overall, the strain intensity factor method shows a fairly good ability in calculating the fatigue crack propagation, especially for the fully reversed cyclic loading condition.

Transition and fracture shift behavior in LCF test of dissimilar welded joint at elevated temperature

This work focused on the low-cycle fatigue (LCF) behavior of modified 9Cr/CrMoV dissimilar welded joint at elevated temperature. Narrow gap submerged arc welding (NG-SAW) process via multi-pass and multi-layer techniques was employed to fabricate the welded joint. LCF tests at different strain amplitude range from 0.22% to 0.75% were performed at strain ratio R=−1. The two-slope behavior based on fracture location shift was presented both on the cyclic stress-strain (CSS) curve and Manson-Coffin (M-C) curve, which could be applied to predict the fatigue life more precisely especially at relatively low strain amplitude. The results indicated that the joint failed in CrMoV-base metal (BM) at relatively low strain amplitude below 0.4% while failure shifted to CrMoV-over tempered zone (OTZ) at higher strain amplitude above 0.4%. Fatigue failure occurred in CrMoV-BM at low strain amplitude could be attributed to temperature softening effect in CrMoV-BM combined with cyclic strengthening in CrMoV-OTZ. While CrMoV-OTZ with a comparable number of grain boundaries and much lower hardness than that of CrMoV-BM was deemed to be the weakest zone across the welded joint at higher strain amplitude. EBSD investigations also revealed that CrMoV-BM experienced more fatigue damage at relatively low strain amplitude, while CrMoV-OTZ accumulated more plastic strain at higher strain amplitude.

Life prediction of l6 steel using strain-life curve and cyclic stress-strain curve by means of low cycle fatigue testing

L6 Steel is used as die material in closed die hot forging process. This material is having some unique properties. These properties are due to its composition. Strain softening is the noticeable property of this material. Due to this in spite of cracking at high stress this material gets plastically deformed and encounters loss in time as well as money. Studies of these properties are necessary to nurture this material at fullest extent. In this paper, numerous experiments have been carried on L6 material to evaluate cyclic Stress - strain behavior as swell as strain-life behavior of the material. Low cycle fatigue test is carried out on MTS fatigue test machine at fully reverse loading condition R=-1. Also strain softening effect on forging metal forming process is explained in detail. The failed samples during low cycle fatigue test further investigated metallurgically on scanning electron microscopy. Based on this study, life estimation of hot forging die is carried out and it’s correlation with actual shop floor data is found out. This work also concludes about effect of pre-treatments like nitro-carburizing and surface coating on L6 steel material, to enhance its fatigue life to certain extent.

Effect of tensile dwell on high-temperature low-cycle fatigue and fracture behaviour of cast superalloy MAR-M247

Hot isostatically-pressed, nickel-based superalloy MAR-M247 was tested under fatigue and creep-fatigue conditions. Continuous cycling and cycling with 10min tensile dwells in each cycle were applied in symmetrical strain control cycle with constant total strain amplitude at 900°C in air. Cyclic hardening/softening curves, cyclic stress-strain curves and fatigue life curves were obtained. The introduction of tensile dwells resulted in lower fatigue life in total strain representation. Surface relief, specimen sections and fracture surface observations revealed crack initiation sites, crack density and crack paths, and help to clarify the effect of dwells on fatigue behaviour.

Multiaxial elastoplastic cyclic loading of austenitic 316L steel

Cyclic stress-strain response and fatigue damage character has been investigated in austenitic stainless steel 316L. Hollow cylindrical specimens have been cyclically deformed in combined tension-compression and torsion under constant strain rate condition and different constant strain and shear strain amplitudes. In-phase and 90° out-of-phase cyclic straining was applied and the stress response has been monitored. Cyclic hardening/softening curves were assessed in both channels. Cyclic softening followed for higher strain amplitudes by long-term cyclic hardening was observed. Cyclic stress-strain curves were determined. Study of the surface damage in fractured specimens revealed the types and directions of principal cracks and the sources of fatigue crack initiation in slip bands.

Unusual effect evidenced at the investigations of the mechanical behavior of composite hydrogels under cyclic compression

An unusual type of mechanical behavior was registered while studying the swollen hydrogel compositions “cellulose-polyacrylamide” in the conditions of multiple cyclic compression tests with the broad variation of the deformation speed. While increasing the deformation rate the clearly seen inversion of the positions of compression and decompression parts of the cyclic stress-strain curves was detected. While carrying out the cyclic compression tests with relatively low deformation speed (about 100–200% of the initial sample's height per minute) the well defined hysteresis of the stress-strain curve can de seen and in these conditions the decompression part of the curve is situated inferior the part corresponding to compression. But while increasing the speed of the deformation the tendency to the progressive approach of the compression and decompression curves to each other is clearly seen. This effect results in the full disappearance of the hysteresis at some value of the deformation speed: the decompression curve coincides with the compression curve. Along with the further increase of the deformation speed the hysteresis appears again but the curve corresponding to compression process is situated inferior the curve corresponding to decompression: the “inversion” of the hysteresis was detected. The precise character of this process depends upon the stiffness of the hydrogel under study. Up to date the convincing explanation o this effect can not be put forward. The authors can only present some hypotheses to explain this phenomenon.

Low and high‐cycle fatigue properties of an ultrahigh‐strength TRIP bainitic steel

AbstractThe scope of this study is to characterize the mechanical properties of a novel Transformation‐Induced Plasticity bainitic steel grade TBC700Y980T. For this purpose, tensile tests are carried out with loading direction 0, 45 and 90° with respect to the L rolling direction. Yield stress is found to be higher than 700 MPa, ultimate tensile strength larger than 1050 MPa and total elongation higher than 15%. Low‐cycle fatigue (LCF) tests are carried out under fully reverse axial strain exploring fatigue lives comprised between 102 and 105 fatigue cycles. The data are used to determine the parameters of the Coffin–Manson as well as the cyclic stress–strain curve. No significant stress‐induced austenite transformation is detected. The high‐cycle fatigue (HCF) behaviour is investigated through load controlled axial tests exploring fatigue tests up to 5 × 106 fatigue cycles at two loading ratios, namely R = −1 and R = 0. At fatigue lives longer than 2 × 105 cycles, the strain life curve determined from LCF tests tends to greatly underestimate the HCF resistance of the material. Apparently, the HCF behaviour of this material cannot be extrapolated from LCF tests, as different damage, cyclic hardening mechanisms and microstructural conditions are involved. In particular, in the HCF regime, the predominant damage mechanism is nucleation of fatigue cracks in the vicinity of oxide inclusions, whereby mean value and scatter in fatigue limit are directly correlated to the dimension of these inclusions.

The influence of microstructure on the cyclic deformation and damage of copper and an oxide dispersion strengthened steel studied via in-situ micro-beam bending

Service materials are often designed for strength, ductility, or toughness, but neglect the effects of cyclic time-variable loads ultimately leading to macroscopic mechanical failure. Fatigue originates as local plasticity that can first only be observed on the micro scale at defects serving as stress concentrators such as inclusions or grain boundaries. Thus, a recently developed technique to perform in-situ observation of micro scale bending fatigue experiments was applied. Micro-beams fabricated from copper, single grained and ultrafine grained (ufg), and an oxide dispersion strengthened (ODS) steel were subject to cyclic deformation and subsequent damage. The elastic stiffness, yield strength, dissipated energy, and maximum stress were measured as a function of cycle number and plastic strain amplitude. From these properties, cyclic stress-strain curves were developed. Initial pronounced monotonic hardening and an increasing Bauschinger effect were observed in all samples with increasing strain amplitude. Cyclic stability was maintained until plastic strain amplitudes reached a critical value. At this point, dramatic cyclic softening and microcracking occurred. The critical strain amplitude was found to be approximately 5.4×10−3 for the copper with a refined grain structure and 1.2×10−2 for the steel specimen. Grain rotation and noticeable changes in sub-grain structure were evident in the ufg copper after a critical strain amplitude of εa=8.3×10−3. In-situ micro fatigue bending couples the cyclic evolution of bulk mechanical properties measurements with real-time electron microscopy analysis techniques of damage and failure mechanisms, which renders it a powerful method for developing novel fatigue resistant materials.

Fatigue analysis of notched specimens made of direct-quenched ultra-high-strength steel under constant amplitude loading

Notched specimens made of a direct-quenched ultra-high-strength steel were investigated by applying the different methods available for the stress-strain analysis of notched components. The methods included the linear rule, Neuber's rule and the strain energy density method. The latter two methods were used in modified forms to improve their estimation capabilities under plane strain conditions. Meanwhile, an elastic-plastic finite element model equipped with the stabilized cyclic stress-strain curve as the material response was used to capture the strain values at the notch root required for the life estimation. The most advanced method based on the theory of critical distances, abbreviated as TCD, was utilized as well. This method, using the results of the elastic-plastic finite element model, was able to define a material characteristic length, which is a material constant, regardless of the notch configurations or the number of cycles in a low-cycle regime. The results showed that the finite element analysis and TCD method are able to estimate the lives closest to the experimental values. The TCD method also predicted the lives with the lowest level of unnecessary conservatism, especially in the case of specimens with sharper notches.

Identification of advanced constitutive model parameters through global optimization approach for DP780 steel sheet

Abstract In recent years, in order to improve the precision of the springback prediction, many advanced material constitutive models have been developed to describe the complex material behavior of sheet metal upon load reversals. The Yoshida-Uemori (Y-U) and the homogeneous yield function-based anisotropic hardening (HAH) models are typical models which are able to predict the Bauschinger effect, transient hardening and permanent softening phenomena. The heavy identification efforts raise to be one main chanllenge before their application due to the numerous parameters. Appropriate tests and robust optimal methods are needed to calibrate parameters. In this work, cyclic stress-strain curve of DP780 steel sheets are obtained by tension-compression tests, and then the parameters of modified Y-U and HAH model are identified through global optimization approach. The identified parameters are verified by the comparison between springback results of U-shape draw-bending process and simulation.

Towards prediction of springback in deep drawing using a micromechanical modeling scheme

Abstract Deep drawing is one of the most commonly used sheet metal forming processes, which can produce metal parts at a high rate. One of the major problems in deep drawing is springback, which is mainly elastic deformation occurring when the tool is removed. The focus of this work is the prediction of springback in deep drawing for DC04 steel using a micromechanical modeling scheme. A novel method is used for the characterization of material that leads to cyclic stress-strain curve. Simulations are performed with the Yoshida Uemori (YU) model for the prediction of springback for a U draw-bend geometry. The maximum deviation between the geometries of experiment and the springback simulation for hat geometry is 2.2 mm. It is shown that this micromechanical modeling scheme allows us to relate the influence of the microstructure to the springback prediction.