Experimental study of creep-damage coupling in concrete by acoustic emission technique

In order to design reliable concrete structures, prediction of long term behaviour of concrete is important by considering a coupling between creep and damage. An experimental investigation on the fracture properties of concrete beams submitted to creep bending tests with high levels of sustained load is reported. The influence of creep on the residual capacity and the fracture energy of concrete is studied. The progression of fracture is followed by the measurement of the crack mouth opening displacement during a three-point bending test. The sustained loading seems to increase the flexural strength of concrete, probably because of the consolidation of the hardened cement paste. The acoustic emission (AE) technique is used to perform the characterization of the influence of creep on the crack development. Results give wealth information on the fracture process zone (FPZ) and the propagation of the crack. A decrease in the amplitude distribution of AE hits is observed in the post-peak region for creep specimens. The width of the FPZ also decreases in this later indicating that the material has a more brittle behaviour which may be due to the development of microcracking under creep and the prestressing of the upper zone of the beam.     

SEMI-ELLIPTICAL FATIGUE CRACK GROWTH UNDER ROTATING OR REVERSED BENDING COMBINED WITH STEADY TORSION

Abstract— An analysis of the influence of steady torsion loading on fatigue crack growth rates under rotating or reversed bending is presented. Mixed-mode (I + III) tests were carried out on cylindrical specimens in DIN Ck45k steel and results are compared for two different testing machines: rotary bending and reversed bending obtained by cyclic Mode I (Δ K ₁) with or without superimposed static Mode III ( K _III) loading, simulating the real conditions on power rotor shafts where many failures occur. The growth and shape evolution of semi-elliptical surface cracks, starting from a chordal notch on the cylindrical specimen surface, was measured for several Mode III/ Mode I ratios. Results have shown that the steady Mode III loading superimposed on the cyclic mode I leads to a significant reduction in the crack growth rates. It is suggested that this retardation is related to an increase of plastic zone size near the cylindrical surface in association with the interlocking of rough fracture surfaces, friction and fretting debris, leading to a decrease of the ΔK effective at the crack tip profile due to the "crack closure effect". This work provides a contribution to a better understanding of crack growth rates under mixed-mode load conditions thereby allowing one to predict remaining lifetimes and to estimate the risks of pre-cracked rotor shafts.     

Creep and fracture in concrete: a fractional order rate approach

The paper analyses the interaction between strain-softening and time-dependent behaviour in the case of quasi-static fracture of concrete. A viscous element based on a fractional order rate law is coupled with a micromechanical model for the fracture process zone. This approach makes it possible to include a whole range of dissipative mechanisms in a single rheological element. Creep fracture in mode I conditions is analysed through the finite element method, the cohesive (or fictitious) crack model and a new space and time integration scheme. The comparison with creep tests executed on three-point bending conditions shows a good agreement.     

Creep and fracture in concrete: a fractional order rate approach

The paper analyses the interaction between strain-softening and time-dependent behaviour in the case of quasi-static fracture of concrete. A viscous element based on a fractional order rate law is coupled with a micromechanical model for the fracture process zone. This approach makes it possible to include a whole range of dissipative mechanisms in a single rheological element. Creep fracture in mode I conditions is analysed through the finite element method, the cohesive (or fictitious) crack model and a new space and time integration scheme. The comparison with creep tests executed on three-point bending conditions shows a good agreement.     

Mixed mode fracture energy of sprucewood

The characterization of Mixed Mode (Mode I and Mode II) behaviour of wood was concentrated on concepts of linear fracture mechanics in the past. Using an adopted version of the splitting test it was possible to obtain complete load displacement curves under different Mixed Mode loading cases for crack propagation along the grain. Therefore fracture energy concepts (specific fracture energy) could be used to characterize the material behaviour. Additionally strength parameters were used in order to describe crack initation in two crack propagation systems. The values for specific fracture energies as well as the strength values were compared with pure Mode I fracture tests. Moreover, the size effect under Mixed Mode loading was investigated to guarantee size independent material characterizing values for the specific fracture energies.     

Influence of prior cyclic hardening on high temperature deformation and crack growth in type 316L (N) stainless steel

For power generating equipment subjected to cyclic loading at high temperature, crack growth could arise from the combinations of fatigue and creep processes. There is potential for the material to undergo hardening (or more generally changes of material state) as a consequence of cyclic loading. Results of an experimental study to examine the influence of prior cyclic hardening on subsequent creep deformation are presented for type 316L(N) stainless steel at 600°C. Experiments were also carried out to explore creep crack growth at constant load, and crack growth for intermittent cyclic loading. For the as-received material there is substantial primary creep (hardening) at constant load, while for the cyclically hardened material at constant load the creep curves show recovery, and increasing creep rate with increasing time. Specimens subjected to prior cyclic hardening were also used for a series of creep and creep-fatigue crack growth tests. These tests demonstrated that there was accelerated crack growth compared to crack growth in as-received material.     

Stress Intensity Controlled Kinetic Crack Growth and Stress History Dependent Life Prediction with Statistical Variability

Consistent with viscoelastic behavior, a power law form in terms of the stress intensity factor is used to specify crack kinetics (growth rate) in the central crack problem under Mode I conditions. The crack growth rate is integrated to obtain the crack size and thereby the stress intensity factor as a function of time. The crack is allowed to grow in a controlled, load dependent manner until it reaches the size at which it becomes unstable. The corresponding time at which this occurs is taken as the lifetime of the material under the specified load history. The special cases of constant load (creep rupture) and constant strain rate to failure are found to have a very simple relationship with each other. This lifetime relationship is verified through the comparison with corresponding data upon a polymeric composite. Finally the creep rupture case is generalized to a probabilistic formalism. The theoretically predicted lifetime distribution functions are verified with data, also upon a polymeric composite. Possible extension of the entire formalism to cyclic fatigue in metals is discussed. Dedicated to Professor Z.P. Bažant for his many contributions.     

Characterization of macrocrack propagation under sustained loading in steel fibre reinforced concrete

Preoccupation for improving concrete infrastructure durability has become just as important as safety issues and concrete cracking plays a key role for durability. Despite various studies carried out in the last decade, very little information regarding the propagation of cracking under sustained loading and the physical mechanisms involved is available. In order to address this problem, an experimental study on the propagation of a macrocrack under sustained loading in steel fibre reinforced concrete (SFRC) beams was completed. This article describes the flexural creep tests carried out on 0.7 m long beams. The evolution of the deflection, the crack width and the crack propagation were measured until the specimens’ failure. The results permit the assessment of the influence of initial CMOD and sustained load levels on crack propagation, damage evolution, and the mechanisms leading to the rupture of the beams. In addition, behaviour of beams in sealed and drying hydric conditions with an identical loading history are compared to determine the influence of hydric conditions. The results show that crack propagation governs the failure mechanisms of SFRC beams subjected to high sustained load levels.     

Why are crack paths in concrete and mortar different from those in PMMA?

Experiments by Bazant and Pfeiffer on concrete and mortar seem to indicate that crack growth does not necessarily take place under Mode I conditions. In order to investigate the influence of the material, experiments were carried out in PMMA with similar geometry to that used by Bazant and Pfeiffer and a numerical simulation was made assuming Mode I crack growth. The experimental results for PMMA differ significantly from those in concrete and mortar, but agree closely with the result from the numerical simulations. The difference is believed to be explained by the fact that small-scale yielding conditions are not realized well enough in concrete and mortar. A fairly large region of small cracks probably influences the crack growth direction.     

Tensile and flexural creep rupture tests on partially-damaged concrete specimens

Three series of novel tensile and flexural creep tests on partially-damaged concrete specimens were carried out in order to gain some insight into creep crack growth and failure of strain-softening materials. In the tests, each specimen was initially loaded to a given point in the descending branch and thus had a lower load-carrying capacity than that at the peak-point. Then, the specimen was unloaded and reloaded to sustain a load which was from 70% to 95% of its current load-carrying capacity. Experimental creep curves display a three-stage process, consisting of primary, secondary and tertiary stages, with a decreasing, constant and increasing creep rate, respectively. The secondary stage dominates the whole failure lifetime, whereas both the secondary and tertiary stages are important in terms of creep deformation. Failure life-time seems to be more sensitive to the change of load level in flexural tests rather than in tensile tests. The decrease in load-carrying capacity due to damage tends to result in a shorter failure lifetime and a lower critical load level for creep rupture. The descending branch of the static load-deflection or load-CMOD curve may be used as an envelope criterion for creep fracture.     

Transient crack-tip fields for mixed-mode power law creep

Mixed-mode stationary crack-tip fields are obtained for an elastic-nonlinear viscous power law creeping solid under conditions of plane strain and small-scale creep. Power law exponents of 2 and 5 are considered which are representative of the creep response of a wide range of ceramics and metals. The imposed far-field mixity ranges from pure mode I to pure mode II. Crack tip fields are calculated during the transient regime using a detailed finite element analysis and are shown to be governed by a Hutchinson-Rice-Rosengren type singularity over the inner one fifth of the creep zone. Dominance of universal mixed-mode near-tip fields within the inner creep zone is found for several mixtures of far-field mode I and mode II. The pronounced effects of the amount of mixity on the size and shape of the creep zone as well as on the time required to reach extensive creep conditions are determined. For a creep exponent of 5, it is estimated that the creep zone grows about seven times faster in mode II than in mode I, with a corresponding decrease in the transition time from small-scale to extensive creep. For a creep exponent of 2, the creep zone grows about six times faster in mode II than in mode I. Finally, the mixed-mode creep fields are used to assess possible beneficial effects of crack deflection or branching in metals and ceramics at elevated temperatures.     

Ductile–brittle fatigue and fracture behaviour of aluminium/PMMA bimaterial 3PB specimens

Fracture toughness and fatigue crack growth tests and numerical simulations on 3PB specimens were carried out to study the behaviour of a crack lying perpendicular to the interface in a ductile/brittle bimaterial. Polymethylmethacrylate acrylic (PMMA) and aluminium alloy 2024 T531 were joined together using epoxy resin. A precrack was introduced into the ductile material and tests were carried out to obtain fracture toughness and fatigue properties. The body force method and elastic–plastic finite-element analyses were used to simulate the experimental stress intensity K_I and cracking behaviour under monotonic and cyclic loads. It was found that the bimaterial fatigue crack growth rate is higher than that for monolithic aluminium 2024 but lower than the rate for a monolithic PMMA. This agreed with the trend for the fracture toughness values and was consistent with the numerical method results. The initial Mode I stable ductile cracking in the aluminium appears to ‘jump’ the interface and continues under mixed fracture Mode (I and II) in the PMMA material up to the final failure. A consistency between the simulation methods has indicated that the bimaterial fatigue crack growth is dominantly elastic with a small plastic zone near the crack tip.     

Mixed mode fracture behaviour of steel fibre reinforced concrete

In this paper, results are reported for a series of discrete end hooked and straight fibre pullout tests subjected to mixed mode action with the results compared to that of discrete fibres pulled out in Mode I (tensile) and Mode II (shear) fracture. As has been previously observed from Modes I and II fracture tests, the snubbing effect dominates the behaviour of fibres at large fibre bending angles. At large fibre bending angles, considerable slip and crack separation occurred prior to the fibres being engaged in taking load and fibres that are inclined close to the cracked surface are ineffective in carrying load. The results of the test were compared with the fibre engagement and bond stress models in the Unified Variable Engagement Model (UVEM). A good correlation is observed for the UVEM model with the test data and provides further confirmation of the validity of the UVEM model to predict the mix mode fracture of steel fibre reinforced concrete.     

Issues relating to numerical modelling of creep crack growth

In this paper creep crack growth behaviour of P92 welds at 923 K are presented. Creep crack growth behaviour for P92 welds are discussed with C^* parameter. Creep crack growth behaviour of P92 welds has been compared with that of P91 welds with C^* parameter. NSW and NSW-MOD model were compared with the experimental creep crack growth data. Plane strain NSW model significantly overestimates the crack growth rate, and plane stress NSW model underestimates it. Whilst, NSW-MOD model for plane stress and plane strain conditions gives lower and upper bound of the experimental data, respectively.FE analysis of creep crack growth has been conducted. Constrain effect for welded joints has been examined with C^* line integrals of C(T) specimens. As a result, constant C^* value using the material data of welded joint gives 10 times lower than that of only HAZ property. Whilst, the predicted CCG rates for welded joint are 10 times higher than those for only HAZ properties. Compared with predicted CCG rate from FE analysis and the experimental CCG rate, it can be suggested that creep crack growth tests for lower load level or for large specimen should be conducted, otherwise the experimental data should give unconservative estimation for components operated in long years.     

The fatigue crack direction and threshold behaviour of mild steel under mixed mode I and III loading

As part of a programme to investigate the mixed mode fatigue crack growth threshold behaviour of mild steel, tests were carried out on three-point bend specimens with spark machined initial slits inclined to give mixed Mode I and III displacements. Overall the expected tendency to Mode I crack growth showed as an initial directional discontinuity followed by a smooth rotation of the crack front until it was almost perpendicular to the specimen sides. At a smaller scale, initial crack growth was by the formation of Mode I branch cracks which developed into a ‘twist’ fracture surface consisting of narrow Mode I facets separated by cliffs. The facets eventually grew out and the fracture surface became smooth. The result in the initiation it was necessary to distinguish between the threshold conditions which result in the initiation of crack growth, specimen failure and crack arrest. An envelope based on Mode I branch crack growth provides a reasonable lower bound to the results for crack initiation and specimen failure. The crack arrest threshold results and some of the crack growth threshold results could not be analysed in detail because of lack of appropriate stress intensity factors.     

Loading‐rate dependence of mode I crack growth in concrete

Mode I crack propagation process of concrete under relatively low loading rates which cover four orders of magnitude (0.2 μm/s to 2.0 mm/s) is investigated with three‐point bending (TPB) beams. All measured material properties exhibit rate sensitivity and follow a log‐linear relationship with the loading rate. A rate‐sensitive softening curve is established. The complete load‐crack mouth opening displacement (P‐CMOD) curve, crack propagation length, and fracture process zone (FPZ) length are simulated based on crack growth criterion with the fitted material parameters under those loading rates. Results show that the simulated P‐CMOD curves agree well with those of experimental measurements. It is clear that the peak load increases with the loading rate and so is the critical crack mouth opening displacement. Moreover, under the same load level, the length of the FPZ and the cohesive stress at the initial crack tip also increase with the increasing loading rate.     

Mixed mode fatigue crack propagation in a ferritic–perlitic cold drawn tube

Previous work by the authors has shown that torsional fatigue tests on cold drawn tube specimens with a longitudinal micronotch present both Mode III ahead of the crack tip (throughout the tube thickness) and Mode I at the defect edges. The co-planar Mode III propagation was prevalent and is followed by Mode II crack propagation along the cold drawn direction.In this work, this behaviour is further investigated by a new series of experimental tests together with a finite element analysis. The mechanisms behind this competition between Mode I and Mode III cracks are analysed and some fractographies were performed on run-outs, broken and interrupted tests.Indeed, pure Mode I and pure Mode II crack propagation rates along with mixed mode crack propagation rates are analysed. Finally, the conditions in order to get Mode I crack growth or shear driven propagation are discussed.     

Time-dependent damage in carbon fibre-reinforced polymer composites

Time-dependent damage (matrix cracks) evolution in AS4/3501-6 cross-ply laminates was studied using constant strain rate and constant stress tests. First ply failure stress and strain as well as the matrix crack density at a given stress level were found to be strongly dependent on strain rate. Matrix crack density increased with creep time at a constant stress level. The compliance and creep rate of the laminate increased in the presence of these cracks. These results emphasize the importance of the knowledge of time-dependent damage evolution in a lamina/laminate of a polymer composite for reliable prediction of creep and creep rupture.     

Creep response of GFRP–concrete hybrid structures: Application to a footbridge prototype

Glass fibre reinforced polymer (GFRP) pultruded profiles have been increasingly used in civil engineering structural applications in the past few decades owing to their high strength, low weight and corrosion resistance. Nevertheless, the low material moduli, which makes design most often governed by deformability and instability phenomena, the brittle failure mechanisms and the high initial costs, have been delaying their widespread use. Hybrid GFRP–concrete structural solutions have been proposed to overcome the aforementioned limitations, namely the low material moduli. Furthermore, GFRP material creep models suggest that such hybrid structures may reduce the creep deformations when compared to full GFRP structures. In this context, this paper presents experimental and analytical investigations about the creep behaviour of a hybrid GFRP–concrete footbridge comprising two I-shaped GFRP pultruded profiles and a thin deck made of steel fibre reinforced self-compacting concrete (SFRSCC). The experiments comprised flexural creep tests on a 6.0 m long footbridge prototype subjected to a uniformly distributed load for up to 2642 h, during which deflections and axial deformations were monitored. In order to assess the influence of loading and environmental conditions on the creep behaviour of the structural system, the prototype was tested for three different combinations of load levels and seasons. Experimental results showed that (i) GFRP–concrete hybrid structures lead to a considerable decrease of the creep deformations of GFRP structures and that (ii) environmental conditions significantly influence the viscoelastic response of these hybrid structures. The models proposed, based on the creep response of the constituent materials, were able to predict the observed structural response for the different load levels and environmental conditions with very good accuracy. Therefore, they are proposed to predict the long-term response of GFRP–concrete structures instead of empirical models based on short-term experimental data.     

Hold-time effect of a single overload on crack retardation at elevated temperature

Many studies have shown that the application of a single overload cycle during constant amplitude load cycling will produce crack retardation or delay. At elevated temperature, the delay effect is time-dependent due to creep that occurs during the overload cycle. A simple method is described to estimate the number of delay cycles as a function of hold time. The reduced crack growth rate following an overload is modelled by a modified constant-amplitude crack propagation relationship. The modification consists in the replacement of the crack rate term by a fractional derivative; the order of the derivative being related to the overload ratio. Delay is assumed to be equal to the number of constant amplitude cycles required by the crack tip to traverse the creep-damage zone created by the overload. A simple notch-type analysis is developed to estimate the creep-damage zone. Predictions compared very favorably with experimental results obtained with a side-grooved DCB specimen with a constant-K characteristic for a fine-grain superalloy IN-100 at 1200°F. The applicability of LEFM for crack growth under creep/fatigue conditions is discussed together with the extension of the results to spectrum loading.