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Measurement Uncertainty Evaluation for High Strain Rate Tensile Properties of Auto-body Steel Sheet (자동차용 강판 고속인장물성 데이터의 측정불확도 산출)
Lightweight vehicle design is a recent mega-trend in the auto industries for improvement of fuel effi-ciency to meet consolidated emission-gas regulation. Lightweight design, however, must be accompanied by crashworthiness of auto-body for passenger safety. One of the solutions for the two contradicted problems is to replace conventional steels with lighter and stronger materials such as aluminum alloys and advanced high strength steels (AHSS) in order to achieve both enhanced crashworthiness and lightweight design of auto-body. AHSS and ultra high strength steel (UHSS) have been steadily developed by steel companies and the application of AHSS and UHSS have been rapidly expanded in auto-body structures.
The auto-body design is usually performed to achieve lightweight design with enhanced crashworthi-ness by numerical analyses which require reliable material data of steel sheets. The material properties need to be acquired at a wide range of strain rates. The strain rates in an auto-body at car crash are evaluated in a wide range such that the maximum strain rate reaches to 300/sec–500/sec while the minimum strain rate is near quasi-static. Such variation of strain rates has a significant effect on the material properties of auto-body struc-tures. Generally the flow stress of a steel sheet tends to increase as the strain rate increases. For accurate de-signs and analyses, the material properties of steel sheets in auto-bodies need to be measured at a wide range of strain rates with an appropriate measurement procedure.
Many researchers have studied experimental methods to identify tensile properties of materials at in-termediate strain rates. The servo-hydraulic machine provides the advantages of precise control of the test speed at a wide range of strain rates, resulting that a generous portion of researches have been conducted with hydraulic testing machines for material properties at intermediate strain rates. Such experimental data for the tensile properties have to be acquired considering the standard uncertainty as well as the reliability and the traceability of the experiment. While the standardized test and verification methods have been established for the quasi-static tensile tests, the one for high strain rate tests has not be established. The standard testing method was proposed by ISO 26203-2 for the high strain rate tensile test in 2011, although there is not enough information about reliability assessment of measurement system. After the guide to the expression of uncer-tainty in measurement (GUM) was published, some of researchers conducted estimation of uncertainties in tensile properties. Beside many enthusiastic studies, uncertainty sources in determining the true stress with respect to the true strain have not been investigated at intermediate strain rates.
This paper is concerned with the standard uncertainty of the tensile properties of auto-body steel sheets at intermediate strain rates ranged from 1/sec to 100/sec. A procedure to obtain true stress–true strain data is properly designed for the experiment and data acquisition. An analytic model is then established to evaluate the standard uncertainty of the measurand of the true stress, which is a function of the input quantities: the
tensile load; the initial length, the thickness and width of a specimen; and the deformed length of a specimen. Sources of uncertainties of the input quantities are evaluated for the high speed tensile test with their associat-ed sensitivity coefficients. Uncertainty of the stress data acquired is also considered in the procedure of the fast Fourier transform (FFT) smoothing process used to remove unnecessary signals acquired from experi-ments. Image analysis using a high speed camera is carried out to measure deformation of the specimen dur-ing high speed tensile tests with proper uncertainty evaluation. A combined standard uncertainty is evaluated from the uncertainties of the input quantities as well as the influence factor for the true stress of auto-body steel sheets at intermediate strain rates. Some examples are presented for the standard uncertainty evaluation of auto-body steel sheets such as SPCC, DP590 and TRIP590. The results demonstrate that the standard un-certainty evaluation procedure has been successfully applied to various kinds of steel sheets.
Effects of the uncertainty on the dynamic deformation analysis are investigated using a stochastic approach
which is called Monte Carlo method. The probability distribution of obtained true stress data is defined with
the normal distribution function. The probability distribution function of the true stress is estimated by
combining all probability distribution functions for the input quantities and influence quantities. The
combination of the probability function is shown to be properly approximated with the normal distribution
function. Random samples are generated for the true stress data according to the normal distribution which is
identified with measured true stress and the standard uncertainty. Generated random samples for the true stress
data are applied into two numerical simulations; dynamic buckling analysis of a circular tube and crash analysis of a front side member. The effects of the uncertainty on the numerical analyses are evaluated with statistical observations of the analysis results. The results presented in the Monte Carlo simulations show similar level of variance to that of material properties. Consequently, the true stress data is obtained with properly evaluated measurement uncertainty and the effects induced by variability of material properties is statistically estimated on numerical analyses for crashworthiness evaluation of auto-body parts.