Thomas Svensson

Life cycle assessment of flooring materials: Case study

The environmental impact of the three flooring materials linoleum, vinyl flooring and solid wood flooring during their life cycles was assessed and compared through life cycle assessment (LCA). The scenarios used describe a Swedish situation. Only impacts on the natural environment were studied The quantitative results of the inventory analysis were evaluated by using three different assessment methods. According to the results, solid wood flooring proved to be clearly the most environmentally sound flooring. Linoleum was ranked as more environmentally sound than vinyl flooring, although this was less evident in comparison with ranking the solid wood flooring.

Prediction uncertainties at variable amplitude fatigue

Abstract Predictions of variable amplitude fatigue life suffer from uncertainties originating from different sources. In this paper, important sources are discussed and estimated, by means of a variable amplitude fatigue model, based on level crossing counts and a version of the Palmgren–Miner cumulative damage rule. The influence of random material strength and parameter estimates is treated in certain detail. The use of simple mathematical models in the analysis introduces systematic errors, which are studied here in terms of the uncertainty regarding the crack opening level at variable amplitude. Additional uncertainties occurring in the fatigue design stage, such as load variation and structural component variability, are briefly discussed and exemplified.

A Robustness Approach to Reliability

Reliability of products is here regarded with respect to failure avoidance rather than probability of failure. To avoid failures, we emphasize variation and suggest some powerful tools for handling failures due to variation. Thus, instead of technical calculation of probabilities from data that usually are too weak for correct results, we emphasize the statistical thinking that puts the designers focus on the critical product functions. Making the design insensitive to unavoidable variation is called robust design and is handled by (i) identification and classification of variation, (ii) design of experiments to find robust solutions, and (iii) statistically based estimations of proper safety margins. Extensions of the classical failure mode and effect analysis (FMEA) are presented. The first extension consists of identifying failure modes caused by variation in the traditional bottom–up FMEA analysis. The second variation mode and effect analysis (VMEA) is a top–down analysis, taking the product characteristics as a starting point and analyzing how sensitive these characteristics are to variation. In cases when there is sufficient detailed information of potential failure causes, the VMEA can be applied in its most advanced mode, the probabilistic VMEA. Variation is then measured as statistical standard deviations, and sensitivities are measured as partial derivatives. This method gives the opportunity to dimension tolerances and safety margins to avoid failures caused by both unavoidable variation and lack of knowledge regarding failure processes.

Random Features of the Fatigue Limit

The classical fatigue limit is often an important characteristic in fatigue design regarding metallic material. The limit is usually obtained from a staircase test in combination with some assumption about the statistical distribution of the limit. This distribution can be of a normal, log-normal or of extreme value type and no particular physical argument gives favor to any specific distribution. This leads to a certain ambiguity in the evaluation of test results which forces the designer to introduce large safety factors. In order to find a physically based statistical distribution for use in staircase tests to determine the fatigue limit we present here a random model for the fatigue limit based on the following assumptions; (i) The square root area model according to Murakami and co-workers is valid, (ii) the randomness in the fatigue limit is induced by the randomness of the maximum defect size, (iii) the random maximum defect size has an extreme value distribution of Gumbel type. This leads to the fatigue limit distribution based on Gumbel (FLG), which is recommended to replace the normal distribution in the evaluation of staircase fatigue tests in case of hard materials. It turns out that the skewness of the resulting distribution depends on the coefficient of variation; with a normal-like non-skewed distribution at the coefficient of variation of five percent.

Fatigue life and crack closure in specimens subjected to variable amplitude loads under plane strain conditions

Abstract The propagation of fatigue cracks in specimens subjected to variable amplitude loading under plane strain conditions was investigated experimentally and numerically, to find the influence of the variable amplitude loading on the stabilised crack closure level. Experiments on four-point-bend specimens with a Gurney block load scheme, showed that the crack closure level depends on the crack length but not on the stress range of the fluctuations. Numerical simulations performed in the fatigue crack growth program FASTRAN-II showed good agreement with the experimental results. In addition, statistical uncertainty analyses performed on the fatigue life show that, for technical applications, the uncertainties in initial crack length and load levels have a greater influence on the uncertainty in fatigue life, than the fluctuation level of the load.

Variation mode and effect analysis: an application to fatigue life prediction

We present an application of the probabilistic branch of variation mode and effect analysis (VMEA) implemented as a first-order, second-moment reliability method. First order means that the failure function is approximated to be linear around the nominal values with respect to the main influencing variables, while second moment means that only means and variances are taken into account in the statistical procedure. We study the fatigue life of a jet engine component and aim at a safety margin that takes all sources of prediction uncertainties into account. Scatter is defined as random variation due to natural causes, such as non-homogeneous material, geometry variation within tolerances, load variation in usage, and other uncontrolled variations. Other uncertainties are unknown systematic errors, such as model errors in the numerical calculation of fatigue life, statistical errors in estimates of parameters, and unknown usage profile. By treating also systematic errors as random variables, the whole safety margin problem is put into a common framework of second-order statistics. The final estimated prediction variance of the logarithmic life is obtained by summing the variance contributions of all sources of scatter and other uncertainties, and it represents the total uncertainty in the life prediction. Motivated by the central limit theorem, this logarithmic life random variable may be regarded as normally distributed, which gives possibilities to calculate relevant safety margins.

Second Moment Reliability Evaluation vs. Monte Carlo Simulations for Weld Fatigue Strength

Monte Carlo simulations have become very popular in industrial applications as a tool to study variational influences on reliability assessments. The method is appealing because it can be done without any statistical knowledge and produces results that appear very informative. However, in most cases, the information gathered is no more than a complicated transformation of initial guesses because the statistical distributions of the dominating variational influences are unknown. The seemingly informative result may then be highly misleading, in particular, when the user lacks sufficient statistical knowledge. Instead, in cases where the input knowledge of the distributional properties is vague, it may be better to use a reliability method based on the actual knowledge, often not more than second moment characteristics. This can easily be done by using a method, based on variances, covariances, and sensitivity coefficients. Here, a specific problem of fatigue life of a welded structure is studied by (i) a Monte Carlo simulation method and (ii) a second moment method. Both methods are evaluated on a fatigue strain–life approach and use experimental data showing variation in weld geometry and material strength parameters. The two methods are compared and discussed in view of the engineering problem of reliability with respect to fatigue damage. Copyright

Prediction Of Fatigue Life Based On Level Crossings And Load History

Models commonly used in fatigue life prediction are based on cycles counted in different ways. The most used method is based on Rain Flow counting which takes care of the stress history in a very specific way. This method has three main drawbacks. It is an ad-hoc way to produce cycles from a continuously varying stress curve. It introduces a memory in the cycle counting in a very rigid way and the algorithm is quite complicated. A model based on level crossings is on the other hand easy to apply but the level crossing spectrum does not contain enough information about the stress history. Here a model is proposed where the damage accumulation depends on the actual level crossing and the stress history condensed in a state variable, as well. The proposed model has the following properties. Failure occurs when the total damage exceeds a given value. Every stress change causes a non-negative damage which depends only on the actual stress, its change and the stress state variable. In a specific application the state variable can be interpreted as the opening stress of a crack. The model is time invariant in the sense that the damage does not change if the time scale is transformed. Hence the life is determined by the sequence of maxima and minima of the stress. In general the dynamics of the state variable must be time invariant and stable in the sense that a stationary and ergodic random stress function shall generate a stationary and ergodic state variable. In this case it is possible to predict fatigue life in terms of a damage intensity, which is the expected damage per time unit. Transactions on Engineering Sciences vol 6,

Inter-laboratory comparison of a fatigue test

Abstract This paper describes a fatigue testing inter-laboratory comparison between six Nordic laboratories, which performed fatigue tests on steel specimens. The specimens were tested with three different stress levels (maximum stress) and with a load ratio R = Smin/Smax = 0.1. Each laboratory tested four specimens at each stress level. The participating laboratories reported the results together with the uncertainty of measurement. The calculated results showed a significant difference between laboratories. However, when the differences in modelling were taken into consideration, no significant differences between the laboratories remained. Significant problems connected with calculations of uncertainty of measurement were detected. One of the major conclusions from the study is that it is of great importance how fatigue tests are reported, e.g. the method of modelling. Better knowledge of how to report fatigue tests, including uncertainty of measurement, as well as a more generally accepted way of reporting such tests – and especially how to treat run-outs – would be a great improvement for the customers of the laboratories.