The Scientific Bulletin of VALAHIA University MATERIALS and MECHANICS –Vol. 15, No. 12 DOI 10.1515/bsmm-2017-0002 DATA SCATTERING IN STRENGTH MEASUREMENT OF STEELS AND GLASS/EPOXY COMPOSITE Adrian CATANGIU, Dan Nicolae UNGUREANU, Veronica DESPA Valahia University of Targoviste, Faculty of Materials Engineering and Mechanics, Department of Materials Engineering, Mechatronics and Robotics 13 Aleea Sinaia Street, Targoviste, Romania E-mail: acatangiu@yahoo.co.uk Abstract. The strength of materials is a complex function which involve two main components, material nature and the presence of defects. Usually glasses exhibit a fragile behavior due to a numerous flaws and the effect is a large range of data scattering in tensile strength measurement. The Weibull probability density function was applied to describe the scatter of experimental data in tensile test, which emphasize a difference between variance in case of tensile strength of three stainless steel grades and glass epoxy composite. The main goal is mathematical modeling of those distributions and finding of equations which predict the probability of failure for a sample subjected to a specific stress. Keywords: Weibull distribution function, tensile strength data scattering, glass/epoxy composite, analysis of variance 1. INTRODUCTION Prediction of failure probability under a specific stress level could be an interesting tool in analysis of material behavior. The variability of a material characteristic it can be described by using Weibull distribution function [1] which cover a large scale of application, such as: fatigue performance [2, 3, 4], scatter of fracture toughness [5], probabilistic characterization in different static tests up to failure (four-point bending [6] or tensile test [7]). In this paper, in order to obtain a relationship between stress level and failure probability was used Weibull distribution. For comparison, analysis of experimental data scattering in tensile test was performed also by using normal distribution. The standard Weibull distribution function, which is shown in equation (1) has three parameters.                               x 1 e x ) , , ; x ( f (1) where β - is the shape parameter, δ- is the scale parameter λ is the location parameter of the distribution. Each parameter has a specific significance as function of analyzed application. In case of tensile strength analysis, the current variable x is σ – ultimate tensile strength, λ- location parameter is the level of stress below which no fracture occurs, δ - scale parameter is usually the average of entire data set and shape parameter β (Weibull modulus) is a measure of experimental data scattering. If the general function (1) is customized for distribution of fracture strength, the failure probability of a specimen subjected to stress level σ is given by:                     0 lim e 1 ) , , ; ( F 0 lim (2) Usually, for brittle materials is difficult to estimate a minimum value of tensile strength σ lim under the material does not break certainly and in this case, the location parameter will be set to zero. The same presumption can be also done for other type of materials in case of lack of safety data. The strength of materials is a complex function which involve two main components, material nature and the presence of defects. Usually ceramics and plastic materials exhibit a fragile behavior due to a numerous flaws and the effect is a large range of data scattering in tensile strength measurement. The number of defects is dependent on sample size (large samples could have more defects as smaller ones, short glass fibers have higher strength then longer ones, etc.). For this reason, in case of large size fragile materials samples there is a higher scattering of experimental data in tensile strength measurement than in case of smaller samples [6, 8, 9]. This phenomena (sample volume contribution in data scattering) is shown also in case of high isotropic materials such as stainless steel (Fig.1). 11