Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

Effect of initial hardness on the thermal fatigue behavior of AISI H13 steel by experimental sand numerical investigations

Based on the Uddeholm thermal fatigue test, the mechanism of thermal fatigue crack initiation and propagation and the influence of initial hardness on the thermal fatigue behavior of AISI H13 steel were investigated. Furthermore, an electromagnetic‐thermo‐mechanical coupled finite element model was established to analyze the temperature evolution and stress accumulation in specimen during thermal cycles. The experimental results demonstrate that, after 3000 thermal cycles, the surface hardness of specimen markedly decreases, and the lath martensite structure seems to completely evolve into a mixture of ferrite and irregularly sphere‐like and bar‐like M23C6 and M6C carbides. According to the numerical results, the effective stress of specimen will increase slightly after every thermal cycle. It presents a distinct stress accumulation phenomenon with increasing number of thermal cycles. Especially at the corner of specimen, it is more significant. The thermal fatigue test results also prove that it is a major site where the initiation and propagation of thermal fatigue primary cracks occur. Both the numerical and experimental results suggest that specimen with initial hardness of 46HRC has the slowest stress accumulation rate, the lowest thermal fatigue damage factor, and the longest thermal fatigue life.     

Thermal-shock-induced crack arrest of two low-alloy steels

Tests were performed on a C-Mn-Nb steel (E 36) and a C-Mn-Ni-Mo steel (A 50B) to determine the fracture toughness either at crack initiation, K_1c or at crack arrest, K_1a, under a very severe thermal shock. The experimental set-up was designed in such a way that it could provide enough flexibility to investigate various factors, including the specimen size effect in brittle fracture and the variations of K_1c or K_1a with temperature.

The thermal shock experiments were carried out either on small discs (thickness 19 mm) or on larger cylinders (height 220 mm) with an inner diameter and an outer diameter of 46 or 50 mm and 150 mm respectively, containing at their external periphery either a longitudinal sharp notch (0.04 mm) for the cylinders or a fatigue crack for the discs. These specimens are cooled to liquid nitrogen temperature until a homogeneous temperature distribution is reached. Then they are heated up by an induction coil set in the centre of the inner hole. The induction coils were designed to maintain purely radial heating of the specimens in order to induce axisymmetric thermal stresses. Typically, the experimental set-up is able to develop radial temperature gradients as large as 250°C in 20 s in the large cylinders and 500°C in 5 or 10 s in the thinner discs. Under the influence of these thermal gradients, which produce tensile hoop stress at the external periphery of the specimens, a crack is initiated from the notch or the initial fatigue precrack, which propagates very rapidly (-100 j1s) over a distance of a few centimetres and then stops.

The temperature distribution measured continuously during the experiments is used as the input for the numerical calculations. Finite element method calculations were performed to determine the variations of the hoop stress and those of the stress intensity factor across the wall thickness. Results obtained on both materi.als are given. In A50B steel it is shown that the apparent fracture toughness K_1c determmed on these large test pieces is smaller than the toughness measured on smaller convsntional specimens. This size effect is explained in terms of a local approach of brLttle cleavage fracture based on Weibull statistics.     

Three‐dimensional thermal response and thermo‐mechanical fatigue analysis for a large LCD TV frame mould in steam‐assisted rapid heat cycle moulding

Rapid heat cycle moulding (RHCM) is a newly developed moulding technique to improve the surface appearance of plastic parts and eliminate the polluting secondary operations such as primers and painting. In steam‐assisted RHCM, the mould surface temperature should be thermally cycled by alternatively cycling the high temperature steam and cooling water in the heating/cooling channels of the mould. The mould design is of great importance for RHCM because it not only has a great effect on the heating/cooling efficiency and hence the productivity but also directly affects the mould surface temperature uniformity and accordingly the final part quality. Furthermore, the service life of the RHCM mould with steam heating is also very much dependent on the mould structure or the layout of the heating/cooling channels as the fatigue crack is likely to occur at the wall of the heating/cooling channels under combined thermal cycling and mechanical loading. In this study, an RHCM mould for a type of 52‐inch LCD TV frame was designed. A three‐dimensional (3D) transient thermal analysis was performed to determine the thermal response efficiency of the designed RHCM mould cavity and investigate the factors affecting the heating efficiency. Then, by using the results obtained from the heat transfer simulation, the thermal‐structure coupling analysis comprehensively considering the cavity pressure and clamp force was conducted to analyse the stress distribution in the mould cavity, which is helpful to find the weak position in the mould cavity. We found that the spots where the maximum stresses occur are similar to the region where fatigue cracks come into being in the actual RHCM mould. Based on the simulation results, the mechanism of the cavity cracks formation on the cavity surface was proposed. Finally, the fatigue analysis was conducted to predict the fatigue life of the RHCM mould. The analysis results show that the regions at the top edges of the heating/cooling channels have the lowest fatigue life and safety factor. The discrepancy between the available life predicted by simulation and the actual service life of the RHCM mould is also discussed.     

Evaluation of thermal shock resistance of cordierite honeycombs

A comparative study on thermal shock resistance (TSR) of extruded cordierite honeycombs is presented. TSR is an important property that predicts the life of these products in thermal environments used for automobile pollution control as catalytic converter or as diesel particulate filter. TSR was experimentally studied by quenching (descending test) the heated samples to water or by heating (ascending test) with an oxyhydrogen flame along with crack detection by acoustic emission (AE) method. TSR was also calculated by using coefficient of thermal expansion (CTE), modulus of elasticity (MOE) and modulus of rupture (MOR) of the honeycomb samples. Cordierite honeycombs of 200 and 400 cpsi were used for the above study. It was observed that the trends of TSR were same for both the experimental methods as well as by calculation. The ascending test method showed lower TSR values compared to water quench method due to early detection of cracks by AE. Finite element method (FEM) was also used to evaluate the thermal stress distribution in solid cordierite using thermal shock test data. It was observed that the maximum thermal stress calculated by FEM was lower than the strength of the material; therefore, the solid cordierite did not fail during such tests.     

Analytical calculation of the stress intensity factor in a surface cracked plate submitted to thermal fatigue loading

A stainless steel specimen with a pre-existing surface notch is exposed to a convective medium of cyclic temperature. The history of stress intensity factor of the cracked body for different crack lengths is obtained by a closed-form integration of the stress field, using Duhamel’s theory with principle of superposition and appropriate weight functions. The obtained results are compared with numerical simulations performed with ABAQUS and they appear to be in very good agreement. The stress intensity factor history shows that fatigue behavior does not depend only on temperature amplitude ΔT=T_max-T_min, quenching rate, and duration of thermal shock but also on heating rate and duration.     

Thermal fatigue failure induced by delamination in thermal barrier coating

The paper presents the experimental and theoretical investigation on the thermal fatigue failure induced by delamination in thermal barrier coating system. Laser heating method was used to simulate the operating state of TBC (thermal barrier coating) system. The non-destructive evaluation such as acoustic emission (AE) detect was used to study the evolution of TBC system damage. Micro-observation and AE detect both revealed that fatigue crack was in two forms: surface crack and interface delamination. It was found that interface delamination took place in the period of cooling or heating. Heating or cooling rate and temperature gradient had an important effect on interface delamination cracking propagation. A theoretical model on interface delamination cracking in TBC system at operating state is proposed. In the model, a membrane stress P and a bending moment M are designated the thermal loads of the thermal stress and temperature gradient in TBC system. In this case, the coupled effect of plastic deformation, creep of ceramic coating as well as thermal growth oxidation (TGO) and temperature gradient in TBC system was considered in the model. The thermal stress intensity factors (TSIFs) in non-FGM (functional gradient material) thermal barrier coating system is analytical obtained. The numerical results of TSIFs reveal some same results as obtained in experimental test. The model is based on fracture mechanics theory about heterogeneous materials and it gives a rigorous explanation of delaminations in TBC system loaded by thermal fatigue. Both theoretical analysis and experimental observation reveal an important fact: delaminations are fatigue cracks which grow during thermal shocks due to compressive stresses in the loading, this loads the delaminations cracks in mixed I and II mode.     

Thermal shock cracking of lithium niobate single crystal

The quantitative estimation of failure stress of a lithium niobate (LN) single crystal due to thermal shock was investigated. Cylindrical test specimens were used in the thermal shock tests. The thermal stress of an LN test specimen under conditions of thermal shock cracking was calculated from a computer program which takes account of the crystal anisotropy, using the surface temperature measured in the thermal shock test. Four-point bending tests were also carried out to examine the relationship between the thermal shock cracking and the failure of a small test specimen due to mechanical load. LN single crystals fractured at the cleavage planes {0 1 1 2} in the thermal shock test and the four-point bending test. Although the failure stress data obtained from both tests obey the Weibull distribution, the Weibull distribution depends not only on specimen size but also on loading type. According to the Weibull distribution of thermal shock test data, if the normal stress σ_n acting on the cleavage planes {0 1 1 2} is lower than 10 MPa, the probability of thermal shock cracking becomes very small — less than 2%. This revised version was published online in July 2006 with corrections to the Cover Date.     

Contact thermal shock test of ceramics

A novel quantitative thermal shock test of ceramics is described. The technique employs contact between a metal cooling rod and hot disc-shaped specimen. In contrast with traditional techniques, the well-defined thermal boundary condition allows for accurate analyses of heat transfer, stress, and fracture. Uniform equi-biaxial tensile stresses are induced in the centre of the test specimen. Transient specimen temperature and acoustic emission are monitored continuously during the thermal stress cycle. The technique is demonstrated with soda-lime glass specimens. Experimental results are compared with theoretical predictions based on a finite element method thermal stress analysis combined with a statistical model of fracture. Material strength parameters are determined using concentric ring flexure tests. Good agreement is found between experimental results and theoretical predictions of failure probability as a function of time and initial specimen temperature.     

Evaluation of thermal degradation of unidirectional CFRP rings

We have studied the thermal degradation of unidirectional carbon-FRP (CFRP) rings. First, we developed a method based on the ring tensile test for evaluating hoop directional strength. And we calculated the distribution of hoop stress by a finite-element method considering friction. Then, we measured the thermal reduction of fatigue strength of unidirectional CFRP rings. To evaluate the degradation of fatigue strength, we applied the Arrhenius equation to confirm the relation between temperature and time. Using this evaluation method, we predicted the thermal reduction of fatigue strength under high temperature and long exposure time.     

The use of RF heating for cyclic thermal shock testing

A potential problem with liquid metal fast reactors is that very rapid temperature changes can be imposed on the surfaces of alloy steel structural members, particularly during plant upset conditions. As part of the UK fast reactor programme, a thermal shock rig was built at Harwell to subject cylindrical testpieces made from candidate steels to thermal upshocks and downshocks more severe than those likely to occur on the actual plant. Testing was carried out in air, and high-power radiofrequency electrical heating was chosen to achieve the required upshock heating rates in excess of 15°C S^-l. Cooling rates of similar magnitude were achieved by means of multiple jets of compressed air in which a fine mist of distilled water was entrained.

This paper discusses the thinking behind the concept of the rig, the choice of control system and associated instrumentation together with the experimental programme required to develop the rig into a useful and reliable test facility.

Prior to the construction of the rig, a fast-running finite difference computer code was specially written to carry out the transient thermal and stress calculations to demonstrate the feasibility of the rig and subsequently to analyse the cyclic stress patterns generated during tests.

Over an eight-year period a total of 41 tests have been carried out on 316SS and 9%Cr steels, covering temperatures up to 625°C, cycles up to 10000 and dwell times up to one hour per cycle. Results have been assessed in terms of cycles to crack initiation as functions of cyclic strain range (computed either as elastic or elastic/plastic), upper temperature and hold time. In turn, the data generated have been used to test out ductility exhaustion theories of failure currently being explored within the UK nuclear industry.     

Measurement of thermal diffusivity of solids using infrared thermography

We report measurement of thermal diffusivity of solid samples by using a continuous heat source and infrared thermal imaging. In this technique, a continuous heat source is used for heating the front surface of solid specimen and a thermal camera for detecting the time dependent temperature variations at the rear surface. The advantage of this technique is that it does not require an expensive thermal camera with high acquisition rate or transient heat sources like laser or flash lamp. The time dependent heat equation is solved analytically for the given experimental boundary conditions. The incorporation of heat loss correction in the solution of heat equation provides the values of thermal diffusivity for aluminum, copper and brass, in good agreement with the literature values.     

Determination of thermal stress in concrete pavements by means of measurement of in-situ strains

A new method of determining the thermal stress of concrete pavement in-situ has been developed and applied to engineering practice with success. It consists of three parts:
1. A system of theorems was established on the basis of mathematical modelisation that both temperature and thermal strain were sine functions of t, the time of observation, owing to the daily fluctuations of temperature and consequently the corresponding thermal strain. It was found that there exist a time phase and an angle of axes rotation between temperature and thermal strain.
2. A bridge circuit with a strain block and specially designed equipment 'free body' was introduced. The strain transducer for every test point consists of one strain gauge in the strain block and one in the 'free body', the former is used as the active gauge in the bridge circuit and the latter as the dummy. A temperature probe of resistance type was inserted nearby each of the gauges. Arrangement of observations and procedure of the data treatment were stated.     

A general model for age acceleration during thermal cycling

Conventional practice in evaluating the effect of elevated temperature upon electronic devices in either accelerated testing or stress screening is the use of the Arrhenius reaction rate equation. This equation fails to represent several key aspects of the stress. A general model that includes the reaction rate effects during heating and cooling, the mechanical effects of heating and cooling, and non-constant activation energies is provided here. The model is based upon a general representation of a thermal cycle. Once the general model is constructed, it is shown to accommodate as special cases, acceleration when one or more of the features is assumed absent. An example illustrates this point. Then several uses for the model beyond the computation of the acceleration factor are discussed. It is suggested that the general model can be used to support test design and equipment selection decisions. The model therefore provides a more realistic portrayal of the effects of a thermal cycle and increased decision flexibility in defining thermal stress regimens.     

Effect of environment atmosphere on thermal shock resistance of the ZrB2–SiC–graphite composite

The thermal shock resistance of the ZrB₂–SiC–graphite composite was evaluated by measuring the retention of the flexural strength after the electrical resistance heating to the temperature ranging from 1000 °C up to 2500 °C. The experiment was operated in two different environment atmospheres (pure oxygen and low oxygen partial pressure which mixed O₂ and Ar with 1:9) at total pressure 2000 Pa. The residual strength for the specimen decreased gradually as the temperature increased up to 2200 °C, and it was slightly higher when heated in low oxygen partial pressure environment than in pure oxygen. In contrast to the specimen heated in low oxygen partial pressure environment, the residual strength for the specimen in pure oxygen increased steeply as the temperature increased from 1600 °C up to 1800 °C. The analysis of the SEM observations combined with EDS confirmed that the surface oxidation played a positive role in the thermal shock resistance of the ZrB₂–SiC–graphite composite with different environment atmospheres. The results here pointed out a potential method for charactering the effect of environment atmosphere on thermal shock resistance of the ZrB₂–SiC–graphite composite.     

A finite element analysis of thermal relaxation of residual stress in laser shock processing Ni-based alloy GH4169

The residual stress induced by laser shock processing and the thermal relaxation behaviors of residual stress in Ni-based alloy GH4169 were investigated by means of three-dimensional nonlinear finite element analysis. To study the effect of different given exposure time and different temperatures on residual stress in laser shock processing Ni-based alloy GH4169, Johnson–Cook material model was used in order to account for the nonlinear constitutive behavior. The influence of heating temperature and exposure time on the stress thermal relaxation was studied. It was concluded that stress relaxation mainly occured during the initial period of exposure, and the degree of relaxation increased as the temperature risen. The results would provide a theoretical basis for controlling the laser shock processing and guiding subsequent experiments.     

Effect of heating temperature and magnesium content on the thermal cyclic failure behaviour of ductile irons

Abstract

This study elucidates the effect of residual magnesium content and heating temperature on the thermal cyclic failure behaviour of ductile irons by applying repeated heating and cooling cycles. Five irons with different residual magnesium contents ranging from 0.038 to 0.066 wt-% were obtained by controlling the amount of nodulariser additions. The thermal fatigue cracking behaviour was investigated during thermal cycling from 25°C to 650, 700, 750, and 800°C, respectively. Experimental results indicate that the thermal fatigue cracking resistance of ductile iron decreases with increasing residual magnesium content. The maximum heating temperatures of 700°C and 750°C led to the most severe thermal fatigue cracking in the specimens containing 0.054 wt-% and 0.060 wt-% residual magnesium content. Recrystallisation of ferrite grain occurred when the thermal cycles exceeded a certain number after testing at 800°C, which deferred the initiation of thermal fatigue cracking.     

Numerical computation of thermal fatigue crack growth of cast iron

Thermal fatigue experiments have been carried out on a single‐edge wedge specimen of the SiMo cast iron to reproduce the conditions experienced by exhaust manifolds during operation. The leading edge temperature was cycled between 20 and 750 °C and the temperature distribution on the specimen surface was measured by thermocouples throughout the thermal cycle. Due to the complexity of the loading and interaction effects between cracks, numerical simulation of crack propagation and shielding effects in multicracked structures appear a useful way to analyze this problem. Therefore, 3D thermo‐mechanical computation was performed with the finite element code ABAQUS of both un‐cracked and multicracked specimen. This computation allowed us to assess the temperature, stresses and strains distribution over a thermal fatigue specimen and the estimation of the crack growth rate using the energy criteria based on the calculation of the J‐integral crack tip.     

Fatigue crack propagation under cyclic thermal stress

Structures used at elevated temperature subject to severe cyclic thermal stress. Therefore, accurate prediction procedures for thermal fatigue crack growth should be applied to rationalise component flaw assessment. Fatigue crack propagation tests under thermal stress were carried out using an modified type 316 stainless steel (316FR), which is a candidate material for the fast reactor in Japan. Thermal stress of the tests was generated by cyclically changed temperature distribution through thickness in a plate by induction heating and air-cooling. Numerical analysis was also carried out to examine the applicability of the J integral under cyclic thermal stress. The J integral under elasto-plastic condition under thermal stress is close to the elastically calculated J integral. Prediction by J integral tends to be conservative for deeper cracks, and modification of the J integral value using crack opening ratio gives good agreement with the experimental crack growth.