Isothermal Loading Research Articles

The effect of isothermal mechanical cycling on Cu–13.3Al–4.0Ni (wt.%) shape memory alloy single crystal wires

In this paper, we study the effect of isothermal mechanical loading and unloading followed by thermal recovery on Cu–13.3Al–4.0Ni (wt.%) shape memory alloy single crystal wires. The mechanical loading tests are repeated at an ambient temperature until the stress–strain response stabilizes. This study is carried out at ambient temperatures in the range 25–125 °C, and for an overall strain of 8.62% on one sample and 19.65% on another sample. In either case, the residual inelasticity at the end of thermal recovery was practically non-existent. The evolution of transformation temperatures was also studied, and found not to change significantly over 34 stress cycles at an overall strain of 8.62%. On the other hand, there was an increase in the range, A f– M f, by 8.9 °C over 24 stress cycles at an overall strain of 19.65%. Finally, the stress–temperature phase diagram of the cycled material is given.

Biaxial thermomechanical fatigue on a 304L-type austenitic stainless steel*

Abstract Various components of nuclear power plants are submitted to very sharp multiaxial thermomechanical loadings, due for instance to the incomplete mixing of flows at different temperatures. As an example, thermal fatigue damage has been detected in auxiliary loops of the primary cooling circuits of Pressurized Water Reactors. In particular, crack networks were observed in in-service pipes submitted to thermomechanical loading resulting from cyclic temperature gradients across the wall-thickness of components in 304 L type austenitic stainless steel. The thermal fatigue behaviour of AISI 304 L type steel has been studied using a specific thermal fatigue test, called Splash, developed in order to reproduce experimentally such thermomechanical biaxial loading in the thickness of parallelepipedic specimens. All tests have been performed at a maximum temperature of 320°C, but with different minimum temperatures. First, the morphological characteristics of the growing networks were analysed, in surface and in depth. Crack initiation is multiple and occurs on sliding lines or at material defects. Crack network stabilization is observed after 400 000 cycles at a temperature of 150°C. The maximum depth is 2.5 mm. Secondly, the stability of the thermal-fatigue cracknetworks previously obtained was investigated under additional isothermal mechanical loading (four-point bend tests). Selection mechanisms of a dominating crack are observed, showing a great influence of shielding effects, branching and tortuous path. Comparison of the dominating crack behaviour with one having a single crack initiated at a notch tip reveals a significant delay effect.

Micro-rheometry of pressurized lubricants and micro-nanorheology

In the present study, micro-rheometry of pressurized lubricants employing a diamond-anvil pressure cell and a laser confocal displacement sensor of 0.4 μm resolution was shown. High pressure viscosity was obtained up to 2 GPa at 200°C for traction oils and PFPE oils. The linearity between logarithmic viscosity and pressure is confirmed. Viscosity-pressure coefficient α at room temperature was almost twice larger than that at 100°C. α for hard disk oil, Zdol2000, was 13/GPa at 24°C ~ 5/GPa at 150°C and was similar to that of paraffinic mineral oil. The feature of the obtained high pressure volume was different for each oil up to 6 GPa. Zdol2000 was the most compressible of all the sample lubricants and its high pressure refractive index increased about 10% at 4.8 GPa. Zdol2000 remained transparent up to 4.8 GPa under isothermal loading. Some considerations for lubricant’s micro-nanorheology were also mentioned with high pressure lubricant’s rheology.

Thermomechanical analysis of thermal shock fracture in the brittle/ductile transition zone—Part II: Numerical calculations and interpretation of the test results

The integrity of PWR pressure vessels is assured by keeping the crack tip stress intensity factor below the toughness of the material under monotonic isothermal loading. To study the effects of sudden cooling associated with a thermal gradient, a specially modified compact specimen has been developed. This has been used to carry out tests in the transition zone with different loading-temperature sequences liable to call the conventional criteria into question. The test is described in detail in Part I of this article [Chapuliot S, et al. Thermomechanical analysis of thermal shock fracture in the brittle/ductile transition zone. Part I: Description of the tests. Engng Fract Mech, 72, 2005, 661–73]. The second part describes numerical investigations to estimate the local mechanical fields at the crack tip and the overall parameters of the fracture mechanics. Finite element thermomechanical calculations are used to interpret the results of these new thermal shock tests using the master curve concept [ASTM E 1921–1997. Standard test method for determination of reference temperature To for ferritic steels in the transition range, 1997] and the Beremin statistical model [Beremin FM. A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metall Trans A, 14A, November 1983, 2287–777].

Axisymmetric Plane Stress States of an Annulus Subject to Displacive Shear Transformation

We study the equilibrium stress field in an annulus composed of a material that admits stress-induced displacive phase transformation that preserves volume. A standard example is the austenite to martensite transformation in shape memory alloys. Attention is restricted to isothermal and axisymmetric load increase. The constitutive model follows a standard J2 formulation appropriate for small strains and incorporates a single internal variable (the martensite phase fraction). A plane-stress boundary value problem is analyzed so as to determine the partitioning of the annulus into regions of (pure) austenite, (pure) martensite, and austenite/martensite mixture. Structure maps are presented, giving concise descriptions of the phase partitioning as the loads increase.

Constitutive equations for the viscoplastic-damage behaviour of a rubber-modified polymer

In this work, experimental tests in tension on a RT-PMMA material have been achieved under various constant true strain rates and at room temperature. The volumetric dilatation was determined in real time during the deformation by videomeasurements. The experimental results have revealed the presence of both the nucleation and growth deformation mechanisms. Modified viscoplastic constitutive equations for homogeneous glassy polymers at isothermal loading, including strain softening and strain hardening, are proposed. Such a model is based upon an approach originally developed for metals at high temperature. Next, this modified model is coupled with a micromechanics formulation, using the Gurson–Tvergaard model, to investigate the macroscopic mechanical response of the RT-PMMA. The constitutive relation includes strain softening, strain hardening, strain rate sensitivity and void evolution. In the test conditions, the modified viscoplastic model coupled with the original Gurson–Tvergaard model produce quantitative agreement with experimental observations.

Evidence from Fe‐ and Al‐rich metapelites for thrust loading in the Transangarian region of the Yenisey Ridge, eastern Siberia

AbstractIn the Transangarian region of the Yenisey Ridge in eastern Siberia (Russia), Fe‐ and Al‐rich metapelitic schists of the Korda plate show field and petrological evidence of two superimposed metamorphic events. An early middle Proterozoic event with age ofc.1100 Ma produced low‐pressure, andalusite‐bearing assemblages atc.3.5–4 kbar and 540–560 °C. During a subsequent late Proterozoic event atc. 850 Ma, a medium‐pressure, regional metamorphic overprint produced kyanite‐bearing mineral assemblages that replaced minerals formed in the low‐pressure event. Based on the results of geothermobarometry andP–Tpath calculations it can be shown that pressure increased from 4.5 to 6.7 kbar at a relatively constant temperature of 540–600 °C towards a major suture zone called the Panimba thrust. In order to produce such nearly isothermal loading of 1–7 °C km −1, we propose a model for the tectono‐metamorphic evolution of the study area based on crustal thickening caused by south‐westward thrusting of the 5–7 km‐thick upper‐plate metacarbonates over lower‐plate metapelites with velocity ofc.350 m Myr−1. A small temperature increase (up to 20 ± 15 °C) of the upper part of the overlapped plate is explained by specific behaviour of steady‐state geotherms calculated using lower radioactive heat production of metacarbonates as compared with metapelites. The suggested thermal‐mechanical model corresponds well withP–Tpaths inferred from obtained thermobarometric data and correlates satisfactorily withP–Ttrajectories predicted by other two‐dimensional thermal models for different crustal thickening and exhumation histories.

Damage‐coupled viscoplastic constitutive modeling for solder materials

This paper presents a damage‐coupled viscoplastic constitutive model for characterizing thermomechanical fatigue (TMF) life of solder materials. The model takes into account the effects of microstructure, temperature and strain rate in the development of damage evolution equations. The TMF model is applied to characterize hysteresis loops of two solder materials, 63Sn‐37Pb and 95.5Sn‐3.9Ag‐0.6Cu, under both isothermal and thermomechanical cyclic loads. The TMF life prediction of 63Sn‐37Pb solder has been found to be a successful model, based on the load‐drop criterion, under fatigue loading.

Thermal fatigue crack networks parameters and stability: an experimental study

A thermal fatigue device––called SPLASH––similar to the facility developed by Marsh [Fatigue crack initiation and propagation in stainless steels subjected to thermal cycling, International Conference on Mechanical Behaviour and Nuclear Applications of Stainless Steels at Elevated Temperature, 1981] has been built in CEA/SRMA in 1985. Since then, it was used mostly on austenitic stainless steels to assess the initiation and growth of thermal fatigue crack networks. In 1998, a leak appeared in an auxiliary loop of the primary circuit of a pressurized water nuclear plant in Civaux (France). Thermal fatigue was suspected and studies began on AISI 304 L type austenitic stainless steel. They were eventually compared to results obtained earlier on AISI 316 L(N). First, the initiation conditions were determined and the damage before initiation was qualitatively observed. Then, some crack networks parameters were chosen and quantitatively determined by image analysis. This part of the study was done at the surface, during crack growth, and at the end of the tests, in depth. Finally, the stability of the crack networks obtained by thermal fatigue was tested under isothermal load controlled four point bending fatigue test, and some conclusions were drawn on the mechanisms of propagating crack selection.

Thixoextrusion of an A356 alloy: microstructural studies and high temperature fatigue behaviour

Isothermal tensile, isothermal and thermomechanical fatigue tests were conducted on thixoextruded and permanent mould cast A356 T6 aluminium alloy over a broad range of temperatures. The results revealed a significant decrease in strength parameters at 280°C, for both materials. The fatigue lives of thixoextruded material were substantially higher than those of permanent mould cast samples under isothermal and thermomechanical fatigue loading. At corresponding mechanical and inelastic strain ranges, thermomechanical out-of-phase cycling were higher than in-phase cycling for the alloy. Due to data scatter, the out-of-phase fatigue lives of the permanent mould cast samples and of the thixoextruded samples appeared to be very similar.

An Endochronic Viscoplastic Approach for Materials with Different Behavior in Tension and Compression

To describe viscoplastic materials with different behavior intension and compression via the example of filled PTFE(Polytetrafluorethylen), an endochronic viscoplastic materialmodel is proposed. The approach is based on a rheological modelwithout an elastic range, using a rate-independent elastoplasticelement with an endochronic flow rule and a nonlinear elastic lawin parallel connection with a nonlinear Maxwell model. The SDE(strength differential effect) due to different experimentalresults in tension and compression tests is described by twointernal variables and their evolution equations. Numericalsimulations show that the model can describe the short and longtime material behavior of filled PTFE under isothermal loading inboth, tension and compression.

Stress induced martensitic transformation kinetics of polycrystalline NiTi shape memory alloy

Abstract The variation of semi-empirical volume fraction of martensite as a function of thermodynamic driving force (t.d.f.) is determined based on measurements of pseudo-elastic deformation effects appearing in tubular Ni 51 at.% –Ti specimens submitted to isothermal biaxial proportional loading. To this end a thermodynamic framework developed by one of the authors (B.R.) was employed. These new experimental results when compared with the predictions of specific formal equations for martensitic phase transformation (p.t.) proposed earlier by B.R., indicate the need for modification of the formula describing the kinetics of reverse p.t. (martensite→austenite) associated with the formation of partial hysteresis in stress–strain co-ordinates. The applied method is new and the results are of importance in macroscopic modelling (determination of appropriate sets of constitutive equations) of the pseudo-elastic behaviour of SMA under complex stress state.

Load Relaxation of Helical Extension Springs in Transient Thermal Environments

The load relaxation behavior of small Elgiloy helical extension springs has been evaluated by a combined experimental and modeling approach. Isothermal, continuous heating, and interrupted heating relaxation tests of a specific spring design were conducted. Spring constants also were measured and compared with predictions using common spring formulas. For the constant heating rate relaxation tests, it was found that the springs retained their strength to higher temperatures at higher heating rates. A model, which describes the relaxation behavior, was developed and calibrated with the isothermal load relaxation tests. The model incorporates both time-independent deformation mechanisms, such as thermal expansion and shear modulus changes, as well as time-dependent mechanisms such as primary and steady state creep. The model was shown to accurately predict the load relaxation behavior for the continuous heating tests, as well as for a complex stepwise heating thermal cycle. The model can be used to determine the relaxation behavior for any arbitrary thermal cycle. An extension of the model to other spring designs is discussed.

The isochronous strain energy approach applied to the load–strain–time–temperature behaviour of geosynthetics

The load–strain–time–temperature behaviour of geosynthetics can be determined by a variety of strength-testing methodologies. However, to date it has not been possible to directly compare and correlate the data obtained from different testing regimes in a generally applicable manner. In this paper, a strain energy approach to the characterisation of the load–strain–time–temperature of geosynthetics is developed that is intended to deal with this problem. This approach takes account of the changes in the behaviour of geosynthetics that occur with time, and is called the isochronous strain energy (ISE) approach. The background to the ISE approach is set out and used to compare and correlate the data from various strength tests carried out on a wide range of geosynthetics. This shows that the isothermal load–strain–time behaviour of a geosynthetic can be represented in a generally applicable manner within an ISE–time plot and that temperature effects can be represented within ISE–time–temperature plots. It is shown that the ISE absorbed by a geosynthetic comprises two basic components, the immediately recoverable ISE and the locked-in ISE. Representation of the behaviour of geosynthetics using these two ISE components allows the prediction of their response to any loading regime applied over any time period.

Measurement of Viscosity of Densifying Glass‐Based Systems by Isothermal Cyclic Loading Dilatometry

This study describes the isothermal cyclic loading dilatometry (ICLD) technique to measure the viscosity of glass‐based materials. We demonstrate its merit relative to constant‐load techniques in minimizing the stress history effects (changes in shrinkage anisotropy and sample microstructure) that arise due to the application of an external load. A constant‐load test overestimates the viscosity by an order of magnitude compared with a cyclic load test. To obtain accurate viscosity data, maximum loading rates and longer unloading periods are desirable as they reduce effects of shrinkage anisotropy on viscosity values. Representative data for a low‐temperature cofired ceramic (LTCC) material are reported. Nonparametric statistical tests revealed insignificant differences between the viscosity data sets at 5% significance level and thus indicate good reproducibility of the testing methodology.

A study of transformations in titanium nickelide by simultaneous measurements of strain, electrical resistance and thermal effects

The results of simultaneous measurements of electrical resistance, stress and strain of Ti-Ni alloys at thermocycling and during the isothermal deformation are presented. It is shown that noticeable part of strain recovery in heating takes place before the start of the reverse transformation and is connected with twinning. The isothermal loading initiates the B2↔B19' and R↔B19' transformations and produce almost no effect on the B2↔R transformation. The results of differential thermal analysis during mechanical testing reveal that a stress may be responsible for the variation of the latent heat of the transformation.

An analytical model for thermal stress analysis of multi-layered microelectronic packaging

Compared to numerical methods, analytical solutions can offer a faster and more accurate procedure for obtaining the interfacial stresses in laminated structures. An analytical model for thermal stress analysis of multi-layered thin stacks on a thick substrate under isothermal loading is proposed in this paper. This analytical approach considers each layer as a beam-type plate with orthotropic material properties. Highly sensitive Moiré interferometry is used to validate the model. The strain field in the bi-material interfaces is obtained experimentally. The test data is in good agreement with the proposed analytical solution. Finite element analysis results are also compared with the analytical solution and the test data.

Analysis of the pseudoelastic behavior of a SMA beam by the element-free Galerkin method

This paper studies the numerical simulation of the pseudoelastic behavior of a shape memory alloy (SMA) beam using the element-free Galerkin method. A multi-dimensional SMA thermomechanical constitutive model is used to characterize the SMA material's pseudoelastic behavior. The explicit incremental displacement-based element-free Galerkin formulation is developed by introducing moving least squares shape functions and continuum tangent stiffness tensors into a weak form of equilibrium equation in the referential configuration. An effective approach to enforce essential boundary conditions is introduced. To assess the performance of the proposed scheme in simulating the pseudoelastic behavior, an SMA beam problem is studied with different nodal arrangements and under different temperatures during the isothermal loading–unloading cycle.

The effect of annealing on the nonlinear viscoelastic response of isotactic polypropylene

AbstractThree series of tensile relaxation tests are performed on isotactic polypropylene at room temperature in the vicinity of the yield point. In the first series of experiments, injection‐molded samples are used without thermal pre‐treatment. In the second and third series, the specimens are annealed at 130°C for 4 and 24 hours, respectively. Constitutive equations are derived for the time‐dependent response of semicrystalline polymers at isothermal loading with small strains. A polymer is treated as an equivalent temporary network of macromolecules bridged by junctions (physical cross‐links, entanglements and crystalline lamellae). Under loading, junctions slide with respect to their positions in the bulk material (which reflects the viscoplastic behavior), whereas active strands separate from their junctions and dangling strands merge with the network at random times (which reflects the viscoelastic response). The network is thought of as an ensemble of meso‐regions (MRs) with various activation energies for detachment of chains from temporary nodes. Adjustable parameters in the stress‐strain relations are found by fitting the observations. The experimental data demonstrate that the relaxation spectrum (characterized by the distribution of MRs with various potential energies) is independent of mechanical factors, but is altered at annealing. For specimens not subjected to thermal treatment, the growth of longitudinal strain does not affect the volume fraction of active MRs and the attempt rate for detachment of chains from their junctions. For annealed samples, the concentration of active MRs increases and the attempt rate decreases with strain. These changes in the time‐dependent response are attributed to broadening of the distribution of strengths of lamellae at annealing.

Model for the viscoelastic and viscoplastic responses of semicrystalline polymers

AbstractConstitutive equations are derived for the time‐dependent behavior of semicrystalline polymers at isothermal loading with small strains. A semicrystalline polymer at temperatures above the glass‐transition point for its amorphous phase is thought of as a network of macromolecules bridged by junctions (physical crosslinks, entanglements, and crystalline lamellae) that can slide with respect to their reference positions in the bulk material under straining. The network is assumed to be highly inhomogeneous, and it is modeled as an ensemble of mesoregions (MRs) with various strengths of interchain interaction. Two types of MRs are distinguished: passive, where these interactions prevent detachment of strands from junctions; and active, where active strands separate from junctions and dangling strands merge with the network at random times as they are thermally agitated. The viscoelastic response of a semicrystalline polymer reflects reformation of strands in active MRs, whereas its viscoplastic behavior is associated with sliding of junctions. Stress–strain relations for uniaxial deformation are developed by using the laws of thermodynamics. Adjustable parameters in the constitutive equations are found by fitting experimental data for isotactic polypropylene in a tensile test with a constant strain rate and in tensile relaxation tests at various strains. Fair agreement is demonstrated between the observations and the results of numerical simulation. It is revealed that the viscoplastic flow of junctions strongly affects the rearrangement process in active MRs, whose rate reaches a threshold value in the vicinity of the apparent yield point. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1438–1450, 2003