Assessment of power law creep constants of Gr91 steel using small punch creep tests

A method for determining the power law creep constants using the small punch (SP) creep test is studied. We performed elastic-plastic-secondary creep finite-element (FE) analysis of Gr91 (ASTM A387 GR91 CL2) steel using the properties at 565 °C to investigate the evolution of stress and strain rate at the weakest location of the SP creep specimen, i.e. at the annular region located at about 0.7 mm from the centre of the specimen. Empirical relations that correlate the applied load to the equivalent stress and the punch displacement rate to the equivalent creep strain rate are suggested on the basis of the finite-element stress analysis results. These simple relations enable us to achieve the constitutive relation of equivalent stress and equivalent creep strain rate under small punch creep test condition. To validate this approach, SP creep tests were conducted and creep constants were evaluated by using the proposed relations. These evaluated creep constants were then compared with those measured from standard uniaxial creep test. It is shown that creep constants evaluated from the SP creep test and the proposed method are in a good agreement with those from the uniaxial creep test.     

Use of small specimen creep data in component life management: a review

Small specimen creep testing techniques are novel mechanical test techniques that have been developed over the past 25 years. They mainly include the sub-size uniaxial test, the small punch creep test, the impression creep test, the small ring creep test and the two-bar creep test. This paper outlines the current methods in practice for data interpretation as well as the state-of-the-art procedures for conducting the tests. Case studies for the use of impression creep testing and material strength ranking of creep resistant steels are reviewed along with the requirement for the standardisation of the impression creep test method. A database of small specimen creep testing is required to prove the validity of the tests.     

On the identification of an effective cross section for a cruciform specimen

Biaxial tensile testing of sheet metals is becoming increasingly popular for sheet metal forming. Determining equivalent stresses in biaxial tensile specimens is more complicated than in conventional uniaxial tensile specimens. In the present study, we compare four different approaches to calculate effective stresses during biaxial tensile loading of a cruciform specimen: (a) partial unloading method, where stresses are determined based on force–strain curves; (b) identification with uniaxial tensile testing; (c) an analysis of equivalent biaxial tests; and (d) numerical simulations. Considering experimental results for an AA1050 aluminium alloy and for a low‐carbon steel DC06, we show that, for the cruciform sample studied here, two methods do not yield physically reasonable results: The uniaxial approach does not properly take into account the effect of transverse loading, and the equivalent biaxial approach exhibits uncertainties in strain measurement data. The most comprehensible approach is the numerical method, because it also yields detailed information about the local stress and strain states. The numerical results are in excellent agreement with the partial unloading method in terms of the initial flow stress and of effective stress–strain curves for strains up to 0.02, with both methods predicting a similar effective cross section of 18.0 mm² for the considered specimen.     

Effect of stress regime‐dependent creep behaviour on measurement of creep strain rate based on small specimen techniques

Small specimen creep testing technique has become a hot topic of research as bulk materials are not available in many occasions. The stress distributions in the small specimens such as small punch and 3‐point bending specimens are essentially nonuniform. As it is known, the creep deformation/damage accumulation mechanisms exhibited at a high stress regime are not the same as the ones at a lower stress regime for many engineering alloys. The potential measurement errors because of stress regime‐dependent creep behaviour, however, has not been considered in the determination of the creep parameters based on small specimen testing in the previous studies. In this paper, 2 kinds of materials that show different Norton's parameters at the corresponding stress regimes are examined. A simple case of 2‐bar structure is firstly adopted to illustrate the measurement error of creep strain rate because of stress regime‐dependent creep behaviour. Furthermore, clamped beam bending testing and small punch testing are investigated to demonstrate the significance of measurement error using the same materials. It is shown that an error of more than 8 times may occur near the transition point of creep deformation mechanism depending on specimen types and materials. Attention should thus be paid to the selection of stress level in the small specimen testing to avoid significant measurement errors.     

小冲孔试样弹塑性蠕变损伤的有限元分析

综合考虑了小冲孔试样实验过程中的弹性、塑性及蠕变等因素,采用了Mises型流动法则和改进的K-R蠕变损伤本构方程,建立了ABAQUS有限元模型,模拟计算了550℃三种载荷条件下,Cr5Mo试样的弹塑性蠕变过程,分析试样的中心蠕变挠度、蠕变应变随时间的变化规律,当量应力的分布情况,以及试样的蠕变损伤与位置的关系,同时分析了挠度与应力对网格的敏感性。结果表明:模拟结果与实验结果很接近,且与单轴实验的应变曲线十分相似;整个试样在中心损伤比较严重,呈现明显局部化特征;讨论了试样网格的敏感性,试样半径方向0mm~1mm之内应力变化幅度比较大(除约束点),并且应力的最大值也出现在这个区域,在这个区域进行网格细化提高计算的精确性,而其他区域采用粗网格减少计算成本,达到精确性和经济性的平衡。径向上网格大小对挠度影响比较大,应力对网格大小不敏感。     

Numerical investigation of creep crack growth in cross‐weld CT specimens. Part II: influence of specimen size

A numerical investigation of the influence of specimen size on creep crack growth in cross‐weld CT specimens with material properties of 2.25Cr1Mo at 550 °C is performed. A three‐dimensional large strain and large displacement finite element study is carried out, where the material properties and specimen size are varied under constant load for a total of eight different configurations. The load level is chosen such that the stress intensity factor becomes 20 MPa √m regardless of specimen size. The creep crack growth rate is calculated using a creep ductility‐based damage model, in which the creep strain rate ahead of the crack tip perpendicular to the crack plane is integrated taking the degree of constraint into account. Although the constraint ahead of the crack tip is higher for the larger specimens, the results show that the creep crack growth (CCG) rate is higher for the smaller specimens than for the larger ones. This is due to much higher creep strain rates ahead of the crack tip for the smaller specimens. If, on the other hand, the CCG rate is evaluated under a constant C * condition, the creep crack growth rate is found to be higher for the larger specimens, except when the crack is located in a HAZ embedded in a material with a lower minimum creep strain rate; then, the creep crack growth rate is predicted to be higher for the smaller specimen. In view of these results, it is obvious that the size effect needs to be considered in assessments of defected welded components using results from CCG testing of cross‐weld CT specimens.     

Multi-step Load Impression Creep Tests for a 1/2Cr1/2Mo1/4V Steel at 565°C

Abstract: Impression creep tests under multi-step load conditions were performed for a service-aged 1/2Cr1/2Mo1/4V steel at 565°C, corresponding to uniaxial stresses in the range of 100–150 MPa. Results of the tests have shown that the minimum creep strain rate data of the material, produced from the creep curves obtained under different load histories, are in good agreement. The results obtained indicate that the results from a multi-step load test of an impression creep specimen, which is particularly useful when the test material is very limited, can be used to obtain the secondary creep properties for a material from a very small test sample.     

Damage mechanics based predictions of creep crack growth in 316 stainless steel

This paper describes a novel modelling process for creep crack growth prediction of a 316 stainless steel using continuum damage mechanics, in conjunction with finite element (FE) analysis. A damage material behaviour model, proposed by Liu and Murakami [1], was used which is believed to have advantages in modelling components with cracks. The methods used to obtain the material properties in the multiaxial form of the creep damage and creep strain equations are described, based on uniaxial creep and creep crack growth test data obtained at 600 °C. Most of the material constants were obtained from uniaxial creep test data. However, a novel procedure was developed to determine the tri-axial stress state parameter in the damage model by use of creep crack growth data obtained from testing of compact tension (CT) specimens. The full set of material properties derived were then used to model the creep crack growth for a set of thumbnail crack specimen creep tests which were also tested at 600 °C. Excellent predictions have been achieved when comparing the predicted surface profiles to those obtained from experiments. The results obtained clearly show the validity and capability of the continuum damage modelling approach, which has been established, in modelling the creep crack growth for components with complex initial crack shapes.     

Creep fracture behaviour of SUS304H steel with vanadium addition based on small punch creep testing

The high-temperature creep fracture behaviour and creep strength of SUS 304H containing a minor addition of V were investigated in this study. A series of small punch (SP) creep and uniaxial creep tests were performed at 700 °C. The load and punch displacement rates obtained from the SP creep tests were used to derive conversion equations to determine the equivalent stress and creep strain rates. A converting equation is suggested in this study so that Norton’s secondary power law creep constants obtained from the SP creep testing can be in agreement with those obtained from the uniaxial tensile creep tests. The creep strength of the modified SUS 304H steel containing V was shown to be superior to that without V based on the current results and other available results for type 304H steel.     

Application of the reference stress method for interpreting impression creep test data

Impression creep tests have been performed on a 316-stainless steel at 600°C, for which conventional uniaxial creep test data are available. It is shown that the technique, based on the reference stress approach, for converting impression creep test data to equivalent uniaxial creep data, is accurate. The results show that the impression creep technique can be used for obtaining creep properties for materials which have high creep resistance at high temperature and test pressure conditions. The difficulties and limitations associated with such situations are described and methods of dealing with them are outlined.     

Brittle coating analysis of orthotropic materials

A brittle coating stress analysis technique applicable to orthotropic materials has been developed. The technique has been applied to a unidirectional glass fibre reinforced epoxy. Its behaviour has been studied under uniaxial and biaxial stress fields using cantilever beam specimens and circular disc specimens under diametral compression. Fibre orientation in the specimens has been varied. In each case it has been observed that the cracks represent the direction of principal strains in the specimen material and not the direction of principal stresses. It is also observed that the threshold strain in the coating is not affected by the biaxiality of the stresses in the coating.     

Thickness dependence of Gc for shear lip propagation from a single crack propagation specimen: aluminium 6061-T6 alloy,cold-rolled copper and BPA polycarbonate

Values ofG _c for ductile crack propagation in a series of double cantilever beam specimens, each with a single side groove of constant depth, increase linearly with net section thickness. If a single side groove with linearly varying depth is cut in a double cantilever beam specimen, the tapered net section thickness results in a plastic zone, the crosssection area of which increases linearly with crack length. The attendantG _c increases in proportion to the plastic zone size in such a specimen. A single properly designed tapered section specimen appears to be capable of providing estimates of (a) the dependence of shear lipG _c on shear lip width, (b) the natural shear lip width and shape, and (c) the shear lip plastic strain. G _c and plastic zone data from specimens of both kinds are reported for aluminium 6061-T6 alloy, cold-rolled copper and BPA polycarbonate. Results of uniaxial tensile tests and of centre-notch tensile tests are also reported for comparison purposes.G _cs, plastic zone sizes and plastic zone strains vary from material to material and appear to reflect in part the drawing and necking characteristics seen in uniaxial tensile tests.     

New approach to determine uniaxial creep properties from small punch creep curves

A key issue in the small punch creep test (SPC) is to determine the equivalent stress that results in the same time to rupture in a uniaxial creep test (UAC). A new approach is proposed based on formulas between the ratio of force in SPC to stress in UAC and the deflection at the minimum deflection rate. Another formula is defined between the minimum deflection rate and the minimum strain rate. In both cases, they were created from a large experimental data pool of high temperature creep-resistant steels. The predicted Norton law and the rupture time dependence on stress are in good agreement with the experimental UAC results. In all cases, the predictions using the present approach are much better than those based on Chakrabarty membrane stretch model.     

Size effect of concrete members applied with flexural compressive stresses

In this study, two types of special experiments are carried out to understand flexural compressive strength size effect of concrete members. The first type is an ordinary cylindrical specimen (CS) with a fully penetrated and vertically standing plate type notch at the mid-height of the specimen, which is loaded in compression at the top surface (e.g., in the parallel direction to the notch length). The second type is a general double cantilever beam (DCB), which is compression loaded in axial direction (e.g., in the parallel direction of the notch). For CS, an adequate notch length is taken from the experimental results obtained from the compressive strength experiment of various initial notch lengths. The trial tests to select the effective initial notch length show that CS with an initial notch length approximately greater than four times the maximum aggregate size fails without an additional increased load and in stable manner under Mode I failure mechanism. Therefore, the initial notch length to the maximum aggregate size ratio of 4.0 is used for all size specimens. For DCB, the eccentricity of loading points with respect to the axial axis of each cantilever and the initial notch length are varied. In both specimens, the compressive loads apply flexural compressive stresses on the crack tip region of the specimens. These two types of specimens fail by Mode I crack opening mechanism. By testing 3 geometrically proportional size specimens for CS and DCB, the experimental datum for flexural compression size effect of concrete are obtained. Using the obtained flexural compressive strength size effect datum, regression analyses are performed using Levenberg-Marquardt's least square method (LSM) to suggest new parameters for the modified size effect law (MSEL). The analysis results show that size effect is apparent for flexural compressive strength of specimens with an initial notch. For CS, the effect of initial notch length on flexural compressive strength size effect is apparent. For DCB, flexural compressive size effect is dependent on the eccentricity of loading points with respect to the axial axis of the cantilever beam. In other words, if DCB specimen is applied with greater tensile stress at the crack tip, the size effect of concrete becomes more distinct. The results show that the flexural compressive strength size effect of initial notch length variation of DCB exists but directly dependent on the loading location. This is due to the fact that the sizes of fracture process zone (FPZ) of all DCB specimens are similar regardless of the differences in the specimen slenderness ratio, but the flexural compressive and tensile stress combinations resulting in stress concentration at the crack tip region has direct effect on size effect of concrete members.     

Superplastic power-law creep of Sn–40%Pb–2.5%Sb peritectic alloy

The power law-creep behavior of superplastic Sn–40Pb–2.5Sb alloys with different grain sizes has been investigated at room temperature. Stress exponent values for these alloys have been determined by indentation creep, conventional creep and uniaxial tension tests in order to evaluate the correspondence of indentation creep results with conventional tests. In all cases, the indentation results were in good agreement with each other and with those of the tensile and conventional creep tests. The average stress exponent values of about 2.6 and 3.0 corresponding to the strain rate sensitivity (SRS) indices of 0.33–0.39, depending on the grain size of the materials, indicate that the grain boundary sliding is the possible mechanism during creep deformation of Sn–Pb–Sb alloys. Within limits, the indentation tests are thus considered useful to acquire information on the creep behavior of small specimens of these soft tin–lead–antimony alloys at room temperature. It is also demonstrated that the indentation creep test provides a convenient method to measure SRS and thereby to assess the ability of a material to undergo superplastic deformation.     

A simplified improved beam analysis of the DCB specimen

Large deviations from the simple cantilever beam model have been observed when analysing double cantilever beam tests in composite materials. In the present paper a simplified improved beam model is proposed. The cracked part of the specimen is analysed by means of shear-corrected classical beam theory. The uncracked part is analysed by considering Saint Venant effects and deformation of a beam on an elastic foundation. Superposition of compliances results in a simple closed form expression which can be used to isolate the effects of different material parameters and analytical simplifications. Crack length corrections are discussed as well as the corrections that have to be made when calculating the strain energy release rate. An extensive numerical comparison is made with the more elaborate solutions of Whitney and Williams. Finally, a discussion is made on the relevance of one-dimensional analysis as compared with two- and three-dimensional analyses. The discussion is supported by numerical comparisons.     

Behaviour of S 355JO steel subjected to uniaxial stress at lowered and elevated temperatures and creep

This paper considers main mechanical properties of structural-high strength low alloy (HSLA) S 355JO (ASTM A709 Gr50) steel subjected to uniaxial tensile tests at lowered and elevated temperatures. The engineering stress vs strain diagrams as well as curve’s dependence of ultimate and yield strengths vs both lowered and elevated temperatures are presented. The focus is also on specimen elongations vs temperature at elevated temperatures. Short-time creep tests for selected constant stresses at selected temperatures were curried out. Uniaxial creep behaviour for selected creep test was modeled by the rheological model. The creep curve determined by modeling procedure was compared with experimentally obtained one. Also, notch impact energy test, using Charpy pendulum impact machine was performed and according to the proposed formula, fracture toughness is calculated. All of experimental tests were performed using modern computer directed experimental systems.     

Development of disc bending fatigue test technique for equi-biaxial loading

The disc bending fatigue test technique was developed to investigate the fatigue life under an equi-biaxial loading condition. In this test, a uniform thickness disc specimen was subjected to a bending load by applying air pressure on the specimen surface. Eleven specimens made of Type 316 stainless steel were tested in a room temperature ambient environment. The crack initiation and growth behaviors during the test were observed through a transparent window. The fatigue life was defined when the peak pressure measured near the specimen surface was reduced to 95% of the supplied air pressure. The fatigue life obtained by the disc bending fatigue test was shorter than that obtained by the uniaxial and plate bending fatigue tests for the same principal strain range. It was confirmed that the equi-biaxial loading condition reduced the fatigue life. The finite element analysis together with test results revealed that the crack was initiated at the edge of the specimen when the specimen thickness was less than 1.0 mm. The specimen thickness should be 1.2 mm in order to maximize the strain range at the specimen center. It was concluded that the disc bending fatigue test can derive the fatigue life under an equi-biaxial loading condition, for which strain range is measured at the specimen center.     

Time and temperature dependent mechanical characterization of polymer‐based materials in electronic packaging applications

Abstract

The thermo‐mechanical testing of high performance polyimide films Type HPPST supplied by Dupont^® was conducted at different strain rates and in different temperature environments. The stress‐strain behavior of materials was investigated, and the dependence of Young's modulus on temperature and strain rate is reported. In view of the uncertainty of the Young's modulus determination, the specimens were tested with unloading‐reloading to verify the test results. Constant strain rate uniaxial tensile tests and long‐time creep tests at various temperatures were performed to characterize the time‐temperature‐dependent mechanical property precisely. Cyclic loading tests were also implemented on specimens to investigate cyclic stress‐strain behaviors. This research is expected to enhance finite‐element‐modeling accuracy and characterize material properties precisely.     

Creep crack initiation at a free edge of an interface between submicron thick elements

To clarify the mechanics of time-dependent crack initiation at an interface edge in submicron thick elements due to creep, delamination experiments are conducted using a micro-cantilever bend specimen with a tin/silicon interface edge. After the specimen time-dependently deforms under a constant load, a delamination crack is initiated at the Sn/Si interface edge. In addition, the steady state creep property of Sn is estimated by performing an inverse analysis using a finite element method based on creep deformation experiments conducted for different specimens. Stress analysis using the obtained creep property reveals that stress and strain rate singularities exist at the Sn/Si interface edge under creep deformation. The intensity of the singular field time-dependently increases as the creep region expands, and eventually it becomes a steady state. The stress and strain rate intensities at the steady state correlate well with the crack initiation life, which indicates that the singular stress field near the interface edge governs the creep crack initiation.