Plastic Strain Range Research Articles

A Modified Closed Form Energy Based Framework for Axial Isothermal-Mechanical Fatigue Life Assessment for Aluminum 6061-T6

In the present investigation, the applicability of a previously developed closed form energy based framework to predict low cycle fatigue (LCF) life of aluminum 6061-T6 was extended from room temperature to elevated temperature. The three different elevated temperatures considered in the present investigation were 75 °C, 100 °C, and 125 °C which were below the creep activation temperature for aluminum 6061-T6. Like the room temperature life assessment framework, the elevated temperature life assessment framework involved computation of the Ramberg–Osgood cyclic parameters from the average plastic strain range and the average plastic energy obtained from an axial isothermal-mechanical fatigue (IMF) test. The temperature dependent cyclic parameters were computed for 25 °C (room temperature), 75 °C, and 100 °C and then extrapolated to 125 °C utilizing functions describing the dependence of the cyclic parameters on temperature. For aluminum 6061-T6, the cyclic parameters were found to decrease with increase of temperature in a quadratic fashion. Furthermore, the present energy based axial IMF framework was found to be able to predict the LCF life of aluminum 6061-T6 at both room and elevated temperatures with excellent accuracy.

A numerical study of non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, different authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle, were investigated. It was demonstrated that: i) LEFM concepts are applicable to the problem under study; ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; iii) the ?Keff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level; v) without contact there is no effect of stress ratio on crack tip parameters. Therefore it is proved that the crack closure concept is valid.

A Modified Closed Form Energy Based Framework for Fatigue Life Assessment for Aluminum 6061-T6—Damaging Energy Approach

A previously developed energy based high cycle fatigue (HCF) life assessment framework is modified to predict the low cycle fatigue (LCF) life of aluminum 6061-T6. The fatigue life assessment model of this modified framework is formulated in a closed form expression by incorporating the Ramberg–Osgood constitutive relationship. The modified framework is composed of the following entities: (1) assessment of the average strain energy density and the average plastic strain range developed in aluminum 6061-T6 during a fatigue test conducting at the ideal frequency for optimum energy calculation, and (2) determination of the Ramberg–Osgood cyclic parameters for aluminum 6061-T6 from the average strain energy density and the average plastic strain range. By this framework, the applied stress range is related to the fatigue life by a power law whose parameters are functions of the fatigue toughness and the cyclic parameters. The predicted fatigue lives are found to be in a good agreement with the experimental data.

Determination of Flow Curve by Cylindrical Upsetting Based on the Principle of Virtual Power

In the design of metalworking technologies, one of the most important amount is the flow stress of the material. A few experimental method can be used to measure it. The most commonly used tests to determine the flow curve of materials include upsetting of cylindrical or prismatic specimens, tension or torsion tests. In our work, the determination method of flow curve were investigated based on the principle of virtual power with cold working conditions. The experimental method, cylindrical upsetting, was executed on the Gleeble 3800 thermo-mechanical simulator. The goal was to determine reliable flow curve for large plastic strain. The results showed that reliable flow stress values were obtainable in equivalent plastic strain range of 0 to 0.7 by continuous cylindrical upsetting.

Comparison of the Linear Matching Method to Rolls-Royce's Hierarchical Finite Element Framework for ratchet limit analysis

This paper provides a direct comparison between the Linear Matching Method (LMM) and the numerical procedures currently being employed within the Rolls-Royce Power Engineering (plc) Hierarchical Finite Element Framework (HFEF) for the assessment of shakedown and ratcheting behaviour. These numerical methods include the application of Direct Cyclic Analysis (DCA), utilised in an automated search procedure for load-interaction plot generation and the recently developed Hybrid procedure. The Hybrid procedure is based on a similar premise to the LMM in that the load history is decomposed into cyclic and constant components. The LMM allows for the direct evaluation of shakedown and ratchet limits to be obtained in a traditional Bree load-interaction format, along with the subsequent maximum plastic strain range for low-cycle fatigue considerations. Three problems have been used for comparison in this paper; the classic Bree cylinder, a nozzle-in-sphere with a cold media injection transient typical of nuclear power plant loading and a pressurised two-bar structure for multi-axial failure analysis. The accuracy of each method has been verified using ABAQUS step-by-step inelastic analysis. The variations in the implementation strategies associated with each method have also been discussed along with computational efficiency and effectiveness, which show that the LMM has the significant potential to improve analysis speeds via obtaining the ratchet limit boundary directly for a specified level of cyclic loading, instead of conducting an iterative search procedure.

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔKeff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.

The Design of a Laboratory Test Machine to Simulate Thermal Fatigue in Hot-Working Tool Steels

Abstract A laboratory-scale thermal fatigue simulator has been designed, constructed, and commissioned by the authors for studying thermal fatigue of hot-working tool steels by means of rapid alternated heating and cooling. The basic design features, construction characteristics, and test capabilities of the thermal fatigue simulator are presented in this paper. Thermal fatigue simulations were run on hardened and tempered AISI H13 hot-working tool steel specimens in time-control with heating and cooling times of 15 and 10 s, respectively, and a total number of 500 and 2000 thermal fatigue cycles. The experimental results have demonstrated that the simulator is capable of producing thermal fatigue cracks with the same characteristics of those seen in real industrial hot-working tools. Based on their size and the extent of propagation, a clear distinction between primary, secondary, and craze cracks could be established at the failed surfaces. Additionally, a thermo-mechanical finite element model of the first 10 thermal fatigue cycles was developed to compute the transient temperatures, stresses, and strains distributions within the test specimen during thermal cycling. Based on the model results, the low cycle fatigue life was estimated using the Coffin–Manson equation, which relates the number of cycles to crack initiation to the plastic strain range per cycle. The experimentally obtained fatigue lives were appreciably shorter than the calculated ones, arguably due to surface roughness and oxidation effects.

A Direct Method on the Evaluation of Cyclic Steady State of Structures With Creep Effect

This paper describes a new extension of the linear matching method (LMM) for the direct evaluation of cyclic behavior with creep effects of structures subjected to a general load condition in the steady cyclic state, with the new implementation of the cyclic hardening model and time hardening creep constitutive model. A benchmark example of a Bree cylinder and a more complicated three-dimensional (3D) plate with a center hole subjected to cyclic thermal load and constant mechanical load are analyzed to verify the applicability of the new LMM to deal with the creep fatigue damage. For both examples, the stabilized cyclic responses for different loading conditions and dwell time periods are obtained and validated. The effects of creep behavior on the cyclic responses are investigated. The new LMM procedure provides a general purpose technique, which is able to generate both the closed and nonclosed hysteresis loops depending upon the applied load condition, providing details of creep strain and plastic strain range for creep and fatigue damage assessments with creep fatigue interaction.

Comparison of mechanical and microstructural properties of conventional and severe plastic deformation processes

The effect of the deformation processes on yield stress, Vickers microhardness and dislocation density were investigated using commercial purity (A1050) and alloyed aluminum (Al 6082). For the evolution of the dislocation density X-ray line profile analysis was used. In the large plastic strain range the variation of mechanical and microstructure evolution of A1050 and of Al 6082 processed by equal channel angular pressing are investigated using route BC and route C. In the plastic strain range up to 3 plane strain compression test was used to evaluate mechanical properties. The hardness and the yield stress showed a sharp increase after the first pass. In the case of A1050 it was found that the two examined routes has not resulted difference in the flow stress. In the case of Al 6082 the effect of the routes on the yield stress is significant. The present results showed that in the comparable plastic strain range higher yield stress values can be achieved by plane strain compression test than by ECAP.

True Stress and Shakedown Analysis of Pressure Vessel which under Cyclic Loading to Plastic Deformation

The aim of this study is to discuss the plastic shakedown and true stress of the cyclically loaded pressure vessel. A thin-walled cylinder pressure vessel is made according to actual working state and a water pressure test system is built. The vessel is loaded to different strain levels of plastic deformation first. Then it is loaded cyclically to shakedown state. The relationship between plastic strain and shakedown range is given based on numerous experiments. The constitutive model of the true stress-true strain of the vessel is obtained. The experimental results show that the ratcheting obviously occurred when the vessel is cyclically loaded to plastic deformation. The true stress-strain constitutive model which is presented in this paper can show appropriately the constitutive relation of the vessel when it is under multi-axial stress state. The application of uniaxial shakedown constitutive model has been demonstrated in this study.

Optimizing the Morphology and Stability of Retained Austenite in a δ-TRIP Steel

δ-TRIP is a low-alloy steel in which ferrite persists at all temperatures in the solid-state, with the remaining microstructure consisting of carbide-free bainite and carbon-enriched retained austenite. The present work explores for the first time, how changes in the intercritical annealing temperature and the transformation conditions associated with bainite influence the morphology and stability of the austenite, and hence the behavior of the microstructure during tensile deformation. It is found that the structure can be optimized to consist of a combination of blocky and film austenite that undergo transformation over a range of plastic strains, thus minimizing the possibility of plastic instabilities, and hence imparting considerable strength and uniform elongation.

A unified damage-healing model for laser shock repair of copper film

A healing method for fatigue damage was studied by laser shock peening (LSP) with excimer laser for polycrystalline copper film. It is found that the reduction of plastic strain range due to laser shock peening could be responsible in the improvement of residual fatigue lives for the damaged specimens by LSP, and the degree of reduction in plastic strain range for the damaged specimens by LSP is more evident when the stress range is larger. According to the variation of the fatigue ductility of the specimen before and after LSP, a unified damage-healing model is proposed during the damage-healing process for copper specimens. The predicted lives by the proposed method agree well with the experimental results.

Warm and Hot Upsetting Sliding Test: Tribology of Metal Processes at High Temperature

Identification of friction data at high temperatures is still a critical point in the optimization of forming processes. In the present paper the WHUST (Warm and Hot Upsetting Sliding Test) dedicated to the tribology of metal forming processes at high temperature is presented. The friction test is able to operate according to a large range of plastic strains, contact pressures and temperatures. The methodology to use the friction test to respect contact conditions encountered at the tool/workpiece interface of various industrial forming processes is discussed. Then three designs of experiments are achieved. The first set of experiments is performed to study the effects of the composition of graphite based lubricants on friction of hot forging tool. A particular attention is paid on the volume of lubricant used, the size of graphite particles and the amount of binding agents. The second set of experiments is performed to quantify the ability of two white lubricants to reduce friction and protect tool surface. The first lubricant is a mineral salt; the second one is an organic salt. Tests are performed at 1200°C on AISI 4820 steel specimens, with AISI H11 nitrided steel contactors. Results show the tested white lubricants lead to coefficient of friction in the same range of the graphite lubricant one, but white lubricants lose their ability to reduce friction as soon as the sliding lengths becomes greater to 10mm, where graphite lubricants can undergo sliding length greater than 30mm. The last experiments are performed to qualify a new sol-gel coating deposited on a common tool steel AISI H13. Tests are operated at 1100°C on AISI 4820 steel specimens. After each test, the ability of the coating to reduce friction and prevent metal transfer from specimens to the coated tool surfaces is established.

Fatigue crack retardation by the application of repair coatings to gas pipelines under pressure

We describe additional capabilities of the repair insulation coatings applied to main pipelines (without taking them out of operation) in increasing the durability of these pipelines. As a specific feature of this method, we can mention the retardation of the subsequent propagation of surface fatigue cracks as a result of the artificial formation of the effect of their closure by filling the crack cavity with liquid epoxy resins. After solidification, it plays the role of a wedge decreasing the range of cyclic plastic strains near the crack tip, i.e., the mechanical driving force of fatigue crack growth. By using the obtained experimental results, we analyze the mechanical situation formed at the crack tip by using the outlined method of retardation of the crack growth.

二軸バルジ試験法による高強度鋼板の加工硬化特性の測定と材料モデリング

The deformation behavior of high strength steel sheets with a tensile strength of 590 MPa under biaxial tension was investigated for a strain range from initial yielding to fracture. The test material was bent and laser welded to fabricate a tubular specimen with an inner diameter of 44.6mm, a wall thickness of 1.2mm, and an axial length of 200mm. Multiaxial tube expansion tests were performed using a servo-controlled tension-internal pressure testing machine. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit curve (FLC) and forming limit stress curve (FLSC) of the as-received sheet material, in addition to the contours of plastic work and the directions of plastic strain rates from initial yielding to fracture. Results calculated using the Yld2000-2d yield function with exponents of 6 to 8 provided the closest agreement with the measured work contours and directions of plastic strain rates for a reference plastic strain range of 0.002 ＜ε0p＜ 0.20. It was concluded that the multiaxial tube expansion test is effective for measuring the multiaxial deformation behavior of sheet metals for a wide range of plastic strains.

Multiaxial tube expansion test method for measurement of sheet metal deformation behavior under biaxial tension for a large strain range

A servo-controlled multiaxial tube expansion testing machine was developed to measure the multiaxial plastic deformation behavior of sheet metals for the range of strain from initial yield to fracture. The testing machine is capable of applying arbitrary principal stress or strain paths to a tubular specimen using an electrical, closed-loop servo-control system for axial force and internal pressure, in addition to having a novel strain measurement apparatus for tubular specimens. Tubular specimens with an inner diameter of 44.6mm were fabricated from cold rolled interstitial-free steel sheet with a thickness of 0.7mm by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit curve (FLC) and forming limit stress curve (FLSC) of the as-received sheet material, in addition to contours of plastic work and directions of plastic strain rates. Results calculated using the Yld2000-2d yield function with an exponent of 6 provided the closest agreement with the measured work contours and directions of plastic strain rates for an equivalent plastic strain range of 0.005–0.36. Moreover, a Marciniak–Kuczyński-type forming limit analysis was performed using the most appropriate yield function with the assumption of isotropic hardening; the calculated and measured FLC and FLSC were in fair agreement. Therefore, the multiaxial tube expansion test is effective to measure the multiaxial deformation behavior of sheet metals for a large range of plastic strain.

Non-linear elastic characterisation of a high strength bainitic roller bearing steel

A small but not negligible non-linear elastic behaviour was detected when investigating cyclic uniaxial push–pull experiments on a high strength bainitic steel. Cyclic torsion experiments led to the conclusion that the shear modulus was relatively constant. A non-linear elastic model was implemented where the bulk modulus was extended with a second order term related to the elastic dilatation and where the shear modulus was constant. The material presented a strength differential effect (SDE), with larger yield stress in compression than in tension. Consequently, the non-linear elastic model was combined with a plasticity model that incorporated a Drucker–Prager yield surface, non-associated flow rule and combined non-linear hardening. Expressions that include non-linear elasticity were derived for the elastic–plastic hardening and the compliance tensors. The extended material model predicted the elastic–plastic results from cyclic push–pull experiments. Also, a phenomenological analysis of the cyclic elastic response showed isotropic damage in the elastic moduli. The steady-state damage increased linearly with the cyclic plastic strain range.

Small fatigue crack growth characteristics and fracture surface morphology of low carbon steel in hydrogen gas

Owing to energy conservation and environmental concerns, hydrogen has been suggested as a next-generation energy source. However, hydrogen known to seep into a metal, degrade its strength, and accelerate fatigue crack growth rates. We have investigated the effects of hydrogen gas on the small fatigue crack growth characteristics of low carbon steel JIS S10C by conducting bending fatigue tests on a specimen with a small blind hole and placed in a low-pressure hydrogen environment. The fatigue crack growth rate in hydrogen was higher than that in nitrogen. The fracture surface of the specimen in hydrogen showed intergranular facets in the low- growth-rate range and a quasi-cleavage fracture surface with brittle striations in the high-growth-rate range. The specimen only showed a ductile fracture surface for nitrogen. The small-fatigue-crack growth rate for nitrogen is given by \({dl/dN\propto \Delta \varepsilon_{p}^{n}l}\), where l, N, and \({\Delta \varepsilon_{p}}\) represent the crack length, number of repetitions, and plastic strain range, respectively. This equation was also satisfied for hydrogen, but only over a short strain range from \({\Delta \varepsilon_t = 0.25}\) to 0.37 % in which the fracture surface exhibited intergranular facets and a ductile morphology, but no quasi-cleavage fracture. The exponent n of the equation was 1.22 in nitrogen and 0.66 in hydrogen environment. The small-fatigue-crack growth law can be used for safe material designs in hydrogen environments.

Influence of deformation on the microelectrochemical heterogeneity of welded joints of 17G1SU steel

We study the microelectrochemical characteristics of 17G1SU pipe steel with. welded joints prepared with the help of a UONII-13/55R electrode under deformation. It is shown that the weld does not affect the microelectrochemical heterogeneity of the stress-free steel: ΔE = 20–80 mV. It is also demon strated that its value for steel increases by ∼10 mV in the zone of elastic deformations and by ∼40 mV in the zone of plastic deformations. In the region of concentrated plastic deformation, this quantity increases to ∼250 mV. The increase in the microelectrochemical heterogeneity of welded specimens is especially pronounced in the heat-affected zone: up to ∼130 mV within the range of elastic strains, up to ∼170 mV within the range of plastic strains, and up to ∼300 mV in the region of formation of a neck prior to fracture of the specimen.

Failure mechanisms in thermomechanical fatigue of DS superalloy Rene 80

Directionally solidified Rene 80 superalloy was tested in thermomechanical fatigue (TMF) over the temperature range 500–900°C and plastic strain range from 0·2 to 0·8% using a DSI Gleeble thermal simulator. Thermomechanical testing was carried out on the parent material in the conventional solution treated and aged condition, as well as gas tungsten arc welded with an IN-738 filler, followed by solution treatment and aging. Comparison of the base TMF unwelded alloy with that of the welded and heat treated alloy showed that varying crack initiation mechanisms, notably oxidation either by stress assisted grain boundary oxidation, or associated with grain boundary MC carbides fatigue crack propagation along grain boundaries and creep deformation were operating, leading to different weakest link failure initiation points.On a évalué le superalliage orienté, René 80, par fatigue thermomécanique (TMF) dans la gamme de température de 500 à 900°C et dans une gamme de déformation plastique de 0·2 à 0·8% en utilisant un simulateur thermique Gleeble de DSI. On a effectué l’essai thermomécanique du matériau de base sous condition conventionnelle de mise en solution et vieillissement, ainsi que du matériau soudé au tig avec un métal d’apport IN–738, suivi par mise en solution et vieillissement. La comparaison de l’alliage de base TMF sans soudure à celui de l’alliage soudé et traité thermiquement a montré que des mécanismes variés d’initiation de fissure entraient en jeu. On note l’oxydation, soit oxydation du joint de grain, assistée par la contrainte, ou associée à la propagation de fissure par fatigue de carbures MC de joint de grain le long des joints de grain et déformation par fluage, conduisant à différents points d’initiation de défaillance du plus faible maillon.