Effect of cyclic loading on subsequent creep behaviour and its implications in creep–fatigue life assessment

Abstract

Evaluation of creep–fatigue failure is essential in design and fitness evaluation of high-temperature components in power generation plants. Cyclic deformation may alter the creep properties of the material and taking cyclic effects into account may improve the accuracy of creep–fatigue failure life prediction. To evaluate such a possibility, creep tests were conducted on 316FR and modified 9Cr–1Mo steel specimens subjected to prior cyclic loading; their creep deformation and rupture behaviours were compared with those of as-received materials. It was found that creep rupture life and elongation generally decreased following cyclic loading in both materials. In particular, the rupture elongation of 316FR in long-term creep conditions drastically decreases as a result of being cyclically deformed at a large strain range. Use of creep rupture properties after cyclic deformation, instead of those of as-received material, in strain-based and energy-based life estimation approaches brought about a clear improvement of creep–fatigue life prediction.     

The effect of prior cyclic loading variables on the creep behaviour of ex-service Type 316H stainless steel

Abstract

Initial tests have been conducted for a systematic survey of the effect of prior cyclic loading on subsequent creep properties. Samples of 316H stainless steel were subjected to prior cyclic loading at 550°C at different combinations of strain range and cycles experienced. These samples were then remachined into uniaxial creep specimens and tested under a constant load at 250 MPa at 550°C.

The initial results from specimens subject to prior cyclic loading show significant decreases in the minimum true creep strain rate of between 30 and 94%. A consistent decrease in the minimum creep strain rate was found with increases in both the strain range of the prior cyclic loading and the number of cycles experienced by the sample. In addition, the prior-cyclic loading has significantly changed the shape of the creep curve to varying degrees depending upon the applied cyclic loading.     

Finite deformation cohesive polygonal finite elements for modeling pervasive fracture

In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening–softening–hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range (\(\Delta \hbox {K})\), load ratio (R), number of cycles (N), plastic compressibility (\({\upalpha })\) and material softening on near tip deformation, stress–strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on \(\Delta \hbox {K}\), R, N, \({\upalpha }\) and material softening. For both hardening and hardening–softening–hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress–strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study.     

ON FATIGUE CRACK GROWTH AND STABLE TEARING

Abstract— An experimental and analytical investigation has been performed to examine the effect of concurrent fatigue cycling and stable tearing on the crack growth fracture resistance of EN3A steel at 360°C. The steel was tested in the as-received and hardened conditions, hardening being achieved by pre-cracking at a load comparable to the elastic limit of the test specimens. For each condition of the steel, resistance curves are obtained both with and without concurrent fatigue cycling.
A significant increase in the crack growth rates occurred as a result of concurrent fatigue cycling. The rates are in reasonably close agreement with the values predicted from the sum of the fatigue crack growth and stable tearing components. The J-estimation formula of Ainsworth is used to demonstrate that there is no interaction between stable tearing and fatigue in the tests for the steel in the as-received condition.     

Modelling tail effects in creep-crack initiation and growth for 316L stainless steel

For complex loading history (creep and fatigue) applied to engineering components, assessment procedures generally estimate the crack initiation and growth by using the summation of continuous fatigue and pure creep crack growth rates. This text deals with the pure creep correlation established in laboratory tests and applied to components subjected to creep-fatigue loading. The trend of the creep opening displacement history superimposed onto the crack progress is sufficient to predict what kind of tail effect will occur when plotting ? vs. C*. The exponent of this correlation is demonstrated to be very close to unity, whatever creep stage is concerned. The contribution of either the material behaviour or the crack extension to the ? -C* correlation is discussed.     

An interpretation of the Ct parameter for increasing load conditions

The prior assessment equations for C_t , which is a well-known fracture parameter for characterizing creep and creep–fatigue crack growth rates, have applicability to constant loading conditions only. However, crack growth due to creep can also occur under varying load conditions during a fatigue cycle when the loading (or unloading) rate is slow enough such that creep deformation can occur near the crack tip. Hence, the applicability of the C_t parameter should be extended to varying load conditions.
In this study, a method of extending the use of the C_t parameter to increasing load conditions is proposed. Based on the concept of Irwin's effective crack size, new equations for estimating C_t under increasing load conditions are derived and denoted as ( C_t )_r . Finite element analyses were also performed under various increasing load conditions. From the analysis, the variation of ( C_t )_r values during the load rise period is obtained and the difference between the ( C_t )_r value at the end of the load rise period and the C_t value at the beginning of the succeeding load hold period is discussed. A generalized creep–fatigue crack growth model which employs ( C_t )_r as a parameter characterizing crack growth rate during the rise time is also discussed.     

Damage Field Ahead of a Tensile Crack in an Elastic-Plastic and Viscoplastic Material

This paper investigates the interaction between a macroscopic crack and microscopic damage in an elastic-plastic and viscoplastic material subjected to tensile in-plane loading. The aim is to predict the fracture conditions by accounting for void accumulation in the vicinity of the crack-tip. A power law relates the stress to the strain of the material. The damage, which invokes the growth and coalescence of microvoids, is confined to a small circular zone surrounding the crack-tip. At the onset of crack extension, the applied stress for small-scale and large-scale yielding solutions is found to be proportional to a₀ ^-1/(n+1), where 2a₀is the initial crack length and n is the strain hardening exponent of the material. For small-scale yielding, the conditions required for fatigue crack growth and steady-state creep are determined. In particular, the variations of the normalized crack length with the number of loading cycles and the time required for failure are shown for various strain hardening exponents, applied loading, and material damage parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

A finite element algorithm to study creep cracks based on the creep hardening surface

This work addresses finite element (FE) modelling of creep cracks under reversed and cyclic loads in steels. A constitutive model based on the creep hardening surface developed by Murakami and Ohno has been selected for this purpose. This model is particularly accurate for describing creep under reversed and cyclic loads and requires no additional material constants. An FE algorithm for this model has been derived and implemented into a research code FVP. The algorithm is verified by comparing the numerical predictions with closed form solutions for simple geometries and loading configurations. FE predictions are compared with experimental data for a stationary crack in a compact tension specimen. The stress and strain fields in the vicinity of a crack under a sustained load are compared with those for the intermediate unloading case. Several integral fracture parameters are investigated as to their appropriateness for describing creep cracks under reversed and cyclic loads.     

CLOSURE BEHAVIOUR OF SURFACE CRACKS

Abstract— The fatigue crack closure response was investigated for a surface crack in BS4360 50B structural steel, subjected to (1) constant amplitude loading and (2) constant amplitude loading interrupted by a single peak overload. A variety of compliance techniques was employed to determine closure behaviour. The crack mouth gauge measured the bulk, plane strain closure load, while the near tip strain gauge indicated the surface, plane stress closure response. For constant amplitude loading it was found that the surface regions of a surface crack are closed for a greater portion of the load cycle than the maximum depth point. A single peak overload caused different closure and growth rate transients at the surface of the thumbnail crack and at the maximum depth point. For growth rates above 10^-6 mm/cycle, such behaviour agrees with the response of a through crack when subjected to constant amplitude loading, and a single peak overload.     

ELEVATED TEMPERATURE FATIGUE CRACK GROWTH BEHAVIOR OF Ti-1100

Abstract— The fatigue crack growth behavior of Ti-1100 is analyzed at elevated temperatures to evaluate the effects of mechanical and environmental variables. Experiments conducted over a wide range of frequencies from 0.01 Hz to 200 Hz indicate a strong dependence of the growth rate upon cyclic loading frequency. Superposition of hold time at maximum and minimum loads over a baseline 1.0 Hz cyclic loading frequency produces an insignificant variation in crack growth rate, which may be attributed to the combined effects of enhanced environmental degradation, crack-tip blunting and increased asperity-induced closure level in this material. It is deduced that a hold time at maximum load results in an interaction of the environmental effects with a retardation effect due to crack tip blunting as a consequence of creep under maximum applied load, whereas for hold at minimum loads, extensive crack-branching and micro-cracking appear to enhance crack closure loads resulting in lower crack growth rates. A linear superposition model is employed to account for the complex interactions due to fatigue, creep and environmental degradation.     

Crack growth in discontinuous glass fibre reinforced polypropylene under dynamic and static loading conditions

Crack propagation in single edge notched tensile specimens of isotactic polypropylene reinforced with short E-glass fibres has been investigated under both fatigue and creep loading conditions. Fatigue crack propagation (FCP) experiments have been performed at three different frequencies (0.1, 1, 10 Hz) and at a mean applied tensile load of 1200 N. Isothermal creep crack propagation (CCP) tests have been conducted under a constant tensile applied load of 1200 N at various temperatures in the range from 32 to 60 °C. Analysis of FCP data allowed an estimation of the pure fatigue and pure creep components of the crack velocity under the adopted cyclic loading conditions. Crack growth at low frequencies (0.1 and 1 Hz) is mainly associated with a non-isothermal creep process. At higher frequency (10 Hz), the pure fatigue contribution appeared more pronounced. Finally, the comparison of FCP and CCP as a function of the mean applied stress intensity factor confirmed the major contribution of creep crack growth during FCP process at low frequencies.     

Durability assessment via residual strength and viscoelastic observations on filled rubber compounds

Because rubber compounds are widely used under cyclic loading conditions, such as tire applications, their fatigue behaviour has been studied for a long time. Two main stages are commonly considered in studying rubber fatigue: crack nucleation and crack growth. Not many studies exist on the residual strength of rubber subsequent to fatigue loading. In this study, the residual strength method is used to model fatigue behaviour of carbon black‐filled and silica‐filled styrene‐butadiene rubber (SBR) compounds. Samples are subjected to repeated fatigue loading (ie, nonzero mean stress) using different strain amplitudes and then subjected to uniaxial constant crosshead rate, relaxation, and creep tests to assess their residual strength and viscoelastic behaviours respectively. The residual strength results are compared with typical S‐N curves. Initial relaxation rates, initial creep rates, asymptotic relaxation values, and secondary creep rates are plotted as functions of fatigue cycle number to understand the viscoelastic behaviours of carbon black and silica‐filled SBR compounds as affected by fatigue processes.     

CRACK TIP FIELDS UNDER NON-STEADY CREEP CONDITIONS—II. ESTIMATES OF ASSOCIATED CRACK GROWTH

Abstract— In a companion paper, estimation formulae have been presented for describing the amplitude of the crack-tip fields under load and displacement controlled boundary conditions. In this paper the associated amounts of creep crack growth are derived. For constant loading, it is shown that the transition period before the attainment of steady creep conditions can be neglected provided the accumulated creep strain at a reference stress exceeds the elastic strain at the same stress. Under constant displacement conditions, it is shown that the amount of creep crack growth is limited and can be predicted from the extent of load relaxation due to creep. This result is confirmed by comparison with experimental data.     

Crack tip fields in a viscoplastic solid: monotonic and cyclic loading

The asymptotic stress and strain field near the tip of a plane strain Mode I stationary crack in a viscoplastic material are investigated in this work, using a unified viscoplastic model based on Chaboche (Int J Plast 5(3):247–302, 1989). Asymptotic analysis shows that the near tip stress field is governed by the Hutchinson–Rice–Rosengren (HRR) field (Hutchinson in J Mech Phys Solids 16(1):13–31, 1968; Rice and Rosengren in J Mech Phys Solids 16(1):1–12, 1968) with a time dependent amplitude that depends on the loading history. Finite element analysis is carried out for a single edge crack specimen subjected to a constant applied load and a simple class of cyclic loading history. The focus is on small scale creep where the region of inelasticity is small in comparison with typical specimen dimensions. For the case of constant load, the amplitude of the HRR field is found to vanish at long times and the elastic K field dominates. For the case of cyclic loading, we study the effect of stress ratio on inelastic strain and find that the strain accumulated per cycle decreases with stress ratio.     

Lifetime evaluation of concrete structures under sustained post-peak loading

Experimental tests on crack propagation in concrete under constant post-peak loading are simulated using the finite element method and the cohesive crack model, in both Mode I and Mixed-mode conditions. The time-dependent behaviour of concrete in the process zone is due to the interaction and growth of microcracks, a phenomenon which, for high constant load levels, turns out to be predominant over linear viscoelastic creep in the bulk material. In mechanical systems based on this type of material behaviour (creep and strain-softening taking place simultaneously), the initial value problem is non-parabolic, i.e., the error at one time level is affected by the accumulation of errors introduced at earlier time levels. Despite these difficulties, the scatter in numerical failure lifetime vs. load level turns out to be negligible in Mode I conditions and practically acceptable in Mixed-mode conditions. Therefore the time-dependent behaviour of the process zone can be inferred solely from the results of direct tensile tests.     

Characterization of the fatigue behaviour of the magnesium alloy AZ91D by means of mechanical hysteresis and temperature measurements

Stress-controlled load increase and constant amplitude tests were performed on the cast magnesium alloy AZ91D. Rather small values of the plastic strain amplitude reflect the very localised plastic deformation predominant in the _I-phase. The cyclic deformation and temperature curves of the load increase tests exhibit cyclic yield strength values which allow a good estimation of the endurance limit. Stress amplitudes above the endurance limit lead to cyclic hardening. As compared to the behaviour under monotonic tensile loading, the alloy exhibits cyclic hardening. Microscopic investigations illustrate the different influences of the - and β-phase in respect to crack initiation.     

Effect of hold time and environment on Fatigue Crack Growth Rate in Ti Alloys

In titanium alloys an effect of hold time at maximum load in a cyclic test is observed if K_max exceeds the threshold for crack propagation at a constant load test. For tests in air it is possible to predict crack growth rate for a hold time cycle from the crack growth rates from a cyclic test with triangular wave form and a constant load test. In 3.5% NaCl solution the measured crack growth rate is lower than the predicted.     

RATE-DEPENDENT DEFORMATION AND FRACTURE OF α-TITANIUM

Aspects of combined rate-dependent deformation and crack growth in α-titanium at room temperature are examined. Results are presented for tests carried out on pre-cracked three point loaded single edge notch bend and compact tension specimens subjected to constant crack opening displacement rates and constant load. Curves of the ratio of the reference stress to the yield stress as a function of the ratio of the plastic displacement to specimen width are found to be different for different rates. The stress difference between continuously loaded curves and curves obtained from load relaxation tests (“relaxed” curves) is found to be similar to uniaxial results. Earlier uniaxial tests show that the “relaxed” curve represents a boundary below which no further creep takes place. The pre-cracked specimen constant load curves cross the “relaxed” curve, even though the contribution from crack growth to the overall deformation is found to be small. Sustained load crack growth is observed to take place under contained yielding conditions and the sustained load resistance curves are found to be different for different reference stresses.     

Fatigue growth of short cracks in Ti-17: Experiments and simulations

The fatigue behaviour of through thickness short cracks was investigated in Ti-17. Experiments were performed on a symmetric four-point bend set-up. An initial through thickness crack was produced by cyclic compressive load on a sharp notch. The notch and part of the crack were removed leaving an approximately 50 μm short crack. The short crack was subjected to fatigue loading in tension. The experiments were conducted in load control with constant force amplitude and mean values. Fatigue growth of the short cracks was monitored with direct current potential drop measurements. Fatigue growth continued at constant R-ratio into the long crack regime. It was found that linear elastic fracture mechanics (LEFM) was applicable if closure-free long crack growth data from constant K_Imax test were used. Then, the standard Paris’ relation provided an upper bound for the growth rates of both short and long crack.The short crack experiments were numerically reproduced in two ways by finite element computations. The first analysis type comprised all three phases of the experimental procedure: precracking, notch removal and fatigue growth. The second analysis type only reproduced the growth of short cracks during fatigue loading in tension. In both cases the material model was elastic-plastic with combined isotropic and kinematic hardening. The agreement between crack tip opening displacement range, cyclic J-integral and cyclic plastic zone at the crack tip with ΔK_I verified that LEFM could be extended to the present short cracks in Ti-17. Also, the crack size limits described in the literature for LEFM with regards to plastic zone size hold for the present short cracks and cyclic softening material.