Constant Life Diagram Research Articles

Comparison of Tensile Fatigue Resistance and Constant Life Diagrams for Several Potential Wind Turbine Blade Laminates

New fatigue test results are presented for four multidirectional laminates of current and potential interest for wind turbine blades, representing three types of fibers: E-glass, WindStrand™ glass, and carbon, all with epoxy resins. A broad range of loading conditions is included for two of the laminates, with the results represented as mean and 95∕95 confidence level constant life diagrams. The constant life diagrams are then used to predict the performance under spectrum fatigue loading relative to an earlier material. Comparisons of the materials show significant improvements under tensile fatigue loading for carbon, WindStrand, and one of the E-glass fabrics relative to many E-glass laminates in the 0.5–0.6 fiber volume fraction range. The carbon fiber dominated laminate shows superior fatigue and static strengths, as well as stiffness, for all loading conditions.

203 一方向CFRPの非主軸疲労強度と等寿命線図の同定(OS6-(1) 複合材料の変形と破壊およびマルチスケール計算技術,オーガナイズドセッション)

203 一方向CFRPの非主軸疲労強度と等寿命線図の同定(OS6-(1) 複合材料の変形と破壊およびマルチスケール計算技術,オーガナイズドセッション)

A study of factors affecting life prediction of composites under spectrum loading

The influence of damage accumulation metric, constant life diagram formulation and cycle counting method on life prediction schemes for composite materials under variable amplitude (VA) loading is investigated in this paper. Special focus is put on residual strength based methodologies; different degradation functions are implemented and compared with the Palmgren–Miner (PM) damage accumulation rule. The predictions are validated by comparison with experimental data from a unidirectional glass/epoxy laminate cycled with three different loading spectra. The effect of constant life diagram (CLD) and cycle counting method used in life prediction is investigated through implementation of alternative existing formulations. Results indicate that a net improvement is achieved when linear strength degradation is implemented as damage metric in life prediction schemes, over the state-of-the-art PM summation. Depending on the spectrum pattern itself, CLD and counting method might be of predominant role; Rainflow counting and the simplistic concept according to which a single S– N curve describes fatigue response of the material under any loading condition (R ratio) are shown to yield consistently best life predictions.

Fatigue strength of metals and composites under repeated high-cycle torsion

The limiting stresses are determined and constant fatigue life diagrams for high-cycle torsion with repeated stress cycle are plotted using the limiting-state models obtained based on the hypothesis of a unified constant-life diagram, which is invariant to the number of cycles to failure. The unified constant-life diagram is given by a transcendental power function whose exponent is an additional parameter characterizing the sensitivity of the material to the asymmetry of the stress cycle. The calculated results and experimental data for carbon and alloyed steels and composite materials are in good agreement

Fatigue Characteristics of Vulcanized Natural Rubber for Antivibration (2nd Report, A Study on the Fatigue Life Prediction Under Uniaxial Variable Loading)

In order to investigate fatigue characteristics of vulcanized natural rubber (NR), fatigue tests are carried out under various stress ratios R and variable loading. In this paper, fatigue crack propagation life is predicted depending on fatigue crack propagation behavior, because the fatigue life is almost the fatigue crack propagation life. Two essential assumptions for the application of Miner's rule are satisfied. It is considered that Miner's rule can predict the fatigue life safely under two-step loading, because the fatigue damage location is depending on R. Under complex variable loading, it is considered that the crack growth rate under 0<R<1 condition is accelerated because of disappearance of crystallization effect. So, it is necessary to make up the modified constant life diagram. The fatigue crack propagation life can be predicted using the modified constant life diagram and Miner's rule.

Fatigue and durability of Nitinol stents

Nitinol self-expanding stents are effective in treating peripheral artery disease, including the superficial femoral, carotid, and renal arteries. However, fracture occurrences of up to 50% have been reported in some stents after one year. These stent fractures are likely due to in vivo cyclic displacements. As such, the cyclic fatigue and durability properties of Nitinol-based endovascular stents are discussed in terms of an engineering-based experimental testing program. In this paper, the combined effects of cardiac pulsatile fatigue and stent-vessel oversizing are evaluated for application to both stents and stent subcomponents. In particular, displacement-controlled fatigue tests were performed on stent-like specimens processed from Nitinol microtubing. Fatigue data were collected with combinations of simulated oversizing conditions and pulsatile cycles that were identified by computer modeling of the stent that mimic in vivo deformation conditions. These data are analyzed with non-linear finite element computations and are illustrated with strain-life and strain-based constant-life diagrams. The utility of this approach is demonstrated in conjunction with 10 million cycle pulsatile fatigue tests of Cordis SMART Control ® Nitinol self-expanding stents to calculate fatigue safety factors and thereby predict in vivo fatigue resistance. These results demonstrate the non-linear constant fatigue-life response of Nitinol stents, whereby, contrary to conventional engineering materials, the fatigue life of Nitinol is observed to increase with increasing mean strain.

Fatigue of sisal fibre reinforced composites: Constant-life diagrams and hysteresis loop capture

Composite materials have been manufactured using untreated or 0.06 M NaOH treated sisal fibre bundles in a polyester or epoxy matrix. Mechanical tests have been conducted to establish the static properties of the composites which have been used to calculate the maximum loads used during fatigue testing. Composites containing alkali treated fibre bundles have better mechanical properties than those with untreated fibre bundles. Alkali treatment has the greatest effect for polyester resin matrices. S– N diagrams constructed from fatigue data at stress ratios of R = 0.1 (tension–tension) and R = −1 (reversed loading) show improvement in the fatigue lives of composites following alkali treatment of sisal fibre bundles. Constant-life diagrams for epoxy matrix composites with untreated or alkali treated fibre bundles show the superiority of the alkali treated fibre composites for low cycle fatigue. Composites loaded in tension–tension fatigue ( R = 0.1) exhibit hysteresis loops with diminishing loop area with increasing number of cycles. The composites loaded in reversed loading fatigue ( R = −1) generate loops with increasing loop area with increasing number of cycles. Failure modes in tension–tension and reversed loading are very different with a distinctive buckling failure mode at R = −1.

Constant-life diagram modified for notch plasticity

A modified constant-life Haigh diagram has been formulated to account for plasticity occurring at stress concentrations under cyclic loading at sufficiently high stress ratios. The notch plasticity is assumed to occur within a range of elastic stress concentration factors, k t, and cycles to failure, N f, such that plastic straining occurs only during the first cycle of constant-amplitude cycling and straining remains elastic thereafter. This condition is expected to occur in high cycle fatigue at stress concentrations of moderate k t loaded at high stress ratio. The validity of the model is assessed by means of fatigue data from Ti–6Al–4V notched specimens having a range of k t. The model, purposely kept simple for ease of use as a design tool, is found to capture trends in the fatigue data not predicted using traditional straight-line models on a mean stress versus alternating stress constant-life plot.

Use of modular networks in the building of constant life diagrams

The objective of this paper is to assess the use of new network architectures in modelling and building of constant life diagrams, using a small number of S– N curves in the training set as a continuation of a previously published paper regarding an FNN (feed-forward neural network). Two architectural models of modular networks, one of them with a gating network very popular in the literature and the other one with a gating network that takes into account the type of load applied to the material, were used. As in the previous paper, data on fatigue to constant stress of a fibreglass composite was tested for 12 S– N curves different. Based on the results it was observed that the ANN having the gating network that takes into account the type of load applied is the one which showed more reliable results and that both modular ANN give better results than the FNN.

Artificial neural networks in spectrum fatigue life prediction of composite materials

An artificial neural network has been proved to be a sufficient tool for modelling fatigue life of multidirectional composite laminates made of GFRP composite materials and tested under constant amplitude loading patterns. Modelling efficiency of the network was satisfactory for both on- and off-axis coupons’ life, irrespective of the test conditions, i.e., R-ratio that defines the developed stress state on the coupon. Tension–Tension, Compression–Compression and even Tension–Compression loading patterns were investigated and modelling accuracy of the proposed ANN model was validated. The main benefit of this new modelling tool is that only a small portion, in the range of 40–50%, of the experimental data is needed for the whole analysis. Thus, expensive and time consuming tests required by the conventional way for the establishment of S– N curves could be significantly reduced without significant loss of accuracy. We applied the neural network method using experimental data from two different (in nature) material systems and proved that constant life diagrams (CLDs), which are very useful for the design of structures loaded under variable amplitude loading spectra, can be efficiently modelled using a much smaller set of experimental data compared to that needed for the development of CLDs by the conventional way.

High-Cycle Fatigue Behavior of Type 316L Stainless Steel

High-cycle fatigue tests were conducted to investigate the effects of temperature, stress ratio (R), specimen orientation, welding and specimen size on the fatigue behavior of type 316L stainless steel. The high-cycle fatigue test results indicated that the fatigue limits significantly decreased when the stress ratio (R) decreased. The corresponding fatigue limits were reduced to lower values when tests were conducted at 300 � C, compared to those obtained at room temperature. The fatigue behavior and fatigue limits of standard and subsize specimens were observed to be consistent at both room temperature and 300 � C. The constant life diagram was established from the S–N curves acquired. The fatigue limit strongly depended on the materials strength, which was a function of specimen orientation, test temperature, and welding processes. The dimension of the fatigue damaged area on a fracture surface increased as the stress ratio decreased. In the case of R ¼� 1:0, the fatigue damaged region extended over the whole fracture surface. The subgrain boundaries after high-cycle fatigue tests were clearly demonstrated by their diffraction patterns, which were related to the dynamic recovery of multiple dislocations.

Optimized Constant-Life Diagram for the Analysis of Fiberglass Composites Used in Wind Turbine Blades

Mandell et al. have recently presented an updated constant-life diagram (CLD) for a fiberglass composite that is a typical wind turbine blade material. Their formulation uses the MSU/DOE fatigue data base to develop a CLD with detailed S-N information at 13 R-values. This diagram is the most detailed to date, and it includes several loading conditions that have been poorly represented in earlier studies. Sutherland and Mandell have used this formulation to analyze typical loads data from operating wind farms and the failure of coupons subjected to spectral loading. The detailed CLD used in these analyses requires a significant investment in materials testing that is usually outside the bounds of typical design standards for wind turbine blades. Thus, the question has become: How many S-N curves are required for the construction of a CLD that is sufficient for an “accurate” prediction of equivalent fatigue loads and service lifetimes? To answer this question, the load data from two operating wind turbines and the failure of coupons tested using the WISPERX spectra are analyzed using a nonlinear damage model. For the analysis, the predicted service lifetimes that are based on the CLD constructed from 13 R-values are compared to the predictions for CLDs constructed with fewer R-values. The results illustrate the optimum number of R-values is 5 with them concentrated between R-values of −2 and 0.5, or −2 and 0.7.

Building of constant life diagrams of fatigue using artificialneural networks

The objective of this paper is to demonstrate the applicability of artificial neural networks on building constant life diagrams of fatigue, making it possible to be obtained from a reduced number of S– N curves. In order to demonstrate this applicability, fatigue data at constant stress for 12 different S– N curves was obtained from the literature. Training three S– N curves, for R=10, 2 and 0.1, produces satisfactory results, however when the number of S– N curves is increased, more reliable solutions are obtained.

On the in vitro fatigue behavior of human dentin: effect of mean stress.

Human dentin is susceptible to failure under repetitive cyclic-fatigue loading. This investigation seeks to address the paucity of data that reliably quantify this phenomenon. Specifically, the effect of alternating vs. mean stresses, characterized by the stress- or load-ratio R (ratio of minimum-to-maximum stress), was investigated for three R values (-1, 0.1, and 0.5). Dentin was observed to be prone to fatigue failure under cyclic stresses, with susceptibility varying, depending upon the stress level. The "stress-life" (S/N) data obtained are discussed in the context of constant-life diagrams for fatigue failure. The results provide the first fatigue data for human dentin under tension-compression loading and serve to map out safe and unsafe regimes for failure over a wide range of in vitro fatigue lives (< 10(3) to > 10(6) cycles).

The influence of high R ratio on mild and sharp notched and unnotched fatigue behavior of 1045 steel with three different heat treatments

The objective of this research was to determine fatigue behavior of SAE 1045 steel subjected to very high tensile mean stress for unnotched, mildly notched, and sharply notched test specimens, and to determine if common S– N f and ε– N f mean stress fatigue life models are applicable. High tensile mean stress fatigue tests for R ratios of 0.8 and 0.9 were conducted using unnotched and notched, K t=1.65 and 3.65, axially loaded SAE 1045 steel specimens with hardness levels of Rc=10, 37, and 50. The monotonic notch strength ratio, NSR, for 5 of 6 test conditions was greater than 1, which allowed many notched cyclic test values of S max or S m to exceed the unnotched ultimate tensile strength. Much notched specimen fatigue resistance at these high R ratios was superior to that of unnotched specimens. However, cyclic creep/ratcheting, particularly for Rc=10 and 37, was a predominant cause of failure. Scanning electron microscopy examination revealed many cyclic failures were similar to monotonic failures consistent with cyclic creep/ratcheting measurements. Specimens failed due to either cyclic creep/ratcheting, to an interaction between cyclic creep/ratcheting and fatigue, or to surface fatigue crack nucleation and growth only. Fatigue life calculations based on S– N f and ε– N f models were up to 5 orders of magnitude in error, and thus completely unreasonable at these high R ratios. For a given test condition, this inaccuracy was due to cyclic creep/ratcheting, scatter, notch strengthening, material properties used, inherent inaccuracy of S– N f constant life diagrams at high R ratios, and/or extrapolation of the Ramberg–Osgood equation beyond S u and σ f.

Alternative Fatigue Lifetime Prediction Formulations for Variable-Amplitude Loading

Accurate prediction of lifetime is an increasingly important issue for wind turbine rotor blade materials. Coupon tests with the variable-amplitude standard loading sequences for wind turbines known as WISPER and WISPERX have indicated that the coupon lifetime can be overestimated by one or two orders of magnitude using conventional lifetime prediction formulations. In the actual design, this might be compensated for by conservative design factors covering other aspects such as environmental conditions. These conventional lifetime prediction formulations use Rainflow counting of the load history, a log-log SN-curve (stress- or strain amplitude versus cycles to failure) for R = −1, a linear Goodman diagram as a constant-life diagram, and Miner summation. In this work, possible alternative fatigue formulations to improve lifetime prediction under variable-amplitude loading are investigated. Results of WISPER and WISPERX variable-amplitude tests on a material representative of wind turbine rotor blades are used. Only alternatives for the SN-curve and the constant-life diagram are investigated; Rainflow counting and Miner summation are used in all predictions discussed here. None of the investigated SN-curves unites an apparent correlation of constant-amplitude data with an accurate and/or conservative lifetime prediction, when including them in a classical linear Goodman diagram. However, the lin-log- and log-log SN-curves do yield better predictions in combination with an alternative constant-life diagram.

Constant life diagrams — a historical review

A historical review of the early development of constant life diagrams (variously referred to as Goodman, Smith, Haigh, etc. diagrams) is presented. It is shown that there were two distinct approaches to the formulation of constant life diagrams for fatigue design purposes. The first one was based on Wöhler's fatigue experiments and involved engineering curve fits of the fatigue endurance data. The Launhardt–Weyrauch, Gerber and Johnson formulae are the main representatives of this approach. The second approach is based on the dynamic theory used for bridge design. The Fidler–Goodman formula is an example of this approach. The early proponents of the second approach questioned Wöhler's test results and did not believe that they could be used for design purposes. Finally, the first books on fatigue of metals introduced citation inaccuracies, which were propagated by subsequent authors.

Fatigue properties of jointed wood composites: Part I. Statistical analysis, fatigue master curves and constant life diagrams

The primary aim of this work was to assess the fatigue performance of scarf-jointed laminated wood composites used to manufacture wind turbine blades and establish simple fatigue design procedures. Laminates made from poplar (Populus canadensis/serotina), Khaya (Khaya ivorensis) and beech (Fagus sylvatica), incorporating typical scarf joints, were assessed under reversed loading (R =−1). Scarf joints were found to be great equalizers of fatigue performance for wood species with different static strengths. Poplar was investigated at several other R ratios (+3, −3, −0.84 and 0.33). The application of 95% survival probability limits derived from pooled data increases the statistical reliability of σ–N curves and gives an improved estimate of a material's minimum performance. The σ–N curves derived for all three wood species at R =−1 were normalized with respect to ultimate compressive strength values and found to be practically coincidental. This allowed the derivation of a master curve for a generic scarf-jointed wood laminate under reversed load conditions. This relationship was verified using data from the literature and found to be a good predictor of fatigue performance. The construction of simple triangulated constant life diagrams based on static tensile and compressive tests and fatigue testing at R =−1 brings about a rapid assessment of the overall fatigue performance of any wood composite. These can then be used in the fatigue design or life prediction of wood composites under cyclic loading.

Life prediction for fatigue of T800/5245 carbon-fibre composites: I. Constant-amplitude loading

This paper presents a study of the fatigue behaviour of a [(±45,0 2) 2] s laminate of the T800/5245 composite system. This modern aerospace material consists of high-failure-strain, intermediate-modulus carbon fibres in a toughened bismaleimide resin system. The fatigue response in repeated tension, repeated compression, and mixed tension-compression was determined at constant stress levels over a wide range of R values, and the results are analysed in terms of constant-life diagrams of the kind that can be used to provide design data. The use of such information for life prediction purposes is discussed.

Metal flow of hot form-rolled helical gears and their fatigue strength after carbonizing: Tanaka, T., Matsui, M., Sawamura, M. and Danno, A. J. Jpn. Soc. Technol. Plast.30 (7), 1038–1043, July 1989 (in Japanese)

This paper presents a study of the fatigue behaviour of a [(±45,02)2]s laminate of the T800/5245 composite system. This modern aerospace material consists of high-failure-strain, intermediate-modulus carbon fibres in a toughened bismaleimide resin system. The fatigue response in repeated tension, repeated compression, and mixed tension-compression was determined at constant stress levels over a wide range of R values, and the results are analysed in terms of constant-life diagrams of the kind that can be used to provide design data. The use of such information for life prediction purposes is discussed.