CN105653808A - Specified plasticity extension strength uncertainty evaluation method based on Monte Carlo - Google Patents

Abstract

The invention discloses a specified plasticity extension strength uncertainty evaluation method based on Monte Carlo. The method comprises the following steps that 1, coordinates (FP0.2, deltaLp0.2) of a point where the specified plasticity extends by 0.2% are looked up on a force-extension curve chart, two points 0.1 Fp0.2 and 0.5 Fp0.2 are calculated, and a mathematical model of the specified plasticity extension strength Rp0.2 is built; 2, probability distribution and parameters of the direct input quantity are determined according to known information; 3, two pairs of coordinates are taken at the position, vertically close to the point 0.1 Fp0.2, on a force-extension curve, two pairs of coordinates are taken at the position, vertically close to the point 0.5 Fp0.2, on a force-extension curve, precise coordinates of 0.1 Fp0.2 and 0.5 Fp0.2are obtained through linear interpolation values, fitting is performed to obtain the slope factor K of an elastic deformation section, and repeated probability sampling interpolation fitting is performed to obtain probability distribution of the indirect input quantity K; 4, sampling is performed for M times according to the probability distribution PDF of the input quantity; 5, M model values of the Rp0.2 are calculated, and then an average value, a standard difference and an any probability inclusion interval are calculated. The method has the advantage that the defects existing when the non-proportional extension strength is evaluated through GUM are overcome.

Description

A kind of regulation plastic elongation intensity uncertainty evaluation method based on Monte Carlo

Technical field

The present invention relates to test and measuring field, particularly a kind of regulation plastic elongation intensity uncertainty evaluation method based on Monte Carlo.

Background technology

" uncertainty of measurement represents guide directive/guide GuidetotheExpressionofuncertaintyinMeasuremen " is various countries' unified criterions followed when representing measurement result, domestic metering specification JJF1059.1-2012 " evaluation of uncertainty in measurement and expression " is equal to the GUM method specified, makes China's metering, test that the expression of result is in line with international standards. JJF1059.2-2012 " evaluates uncertainty of measurement by Monte Carlo method " and is the refilling member of JJF1059.1GUM uncertainty evaluation, the adnexa 1 of IDT international standard ISO/IECGUIDE98-3:2008 (GUM): " with the distribution of Monte Carlo method probability of spreading ", the former inapplicable situation of GUM method can be used the distribution of MCM probability of spreading to carry out uncertainty evaluation and expression by this refilling member specified in more detail. When former GUM is suitable for, it is possible to be verified by MCM. MCM is particularly suited for three kinds of situations: 1, measurement model is substantially in non-linear; 2, the probability density function of input quantity is substantially asymmetric; 3, the probability density function of output deviates normal distribution or �� distribution, is especially apparent the occasion of asymmetric distribution.

The enforcement key step of MCM: (1) obtains the probability distribution of input quantity, the i.e. distribution pattern of input quantity and probability parameter; (2) founding mathematical models; (3) input component calculates substantial amounts of output by mathematical model; (4) obtaining the average of output, standard deviation, probability distribution is interval. The probability distribution of input quantity obtains to directly obtain and obtains with indirect calculation, and a part of input quantity is directly read (such as F by puller system_p0.2, �� L), a part of input quantity is to calculate to obtain (such as sectional area S), and a part of input quantity is that matching obtains (such as k), and this is that the uncertainty evaluation of MCM brings some difficulty.

Current R_p0.2The commonly used GUM method of uncertainty evaluation, partial uncertainty includes: puller system force value detection uncertainty, puller system calibration uncertainty, specimen size uncertainty of measurement, the original gauge length uncertainty of extensometer and note of extending extend uncertainty of measurement, result revision of the convention uncertainty and determine the uncertainty that slope baseline introduces. Problems existing is as follows: 1, GB/T228.1-2010 " metal material stretching test part 1: room temperature test method " uses 10 samples to obtain the measured value of each mechanical performance index, carry out GUM uncertainty evaluation, but often only have two samples during actual tests, need first to do uncertainty evaluation with 10 parallel samples, take relative standard uncertainty to convert, the uncertainty low precision of evaluation when measured value difference is bigger; 2, Wang Jun proposes under the premise of a sample detection in paper " metal material Proof strength of non-proportional measuring result uncertainty ", the slope k taking 100 coordinate points matching stretch sections on power-extension curve carries out the nonproportional cyclic straining evaluation of GUM method, the coordinate that reality takes 100 points on a power-extension curve is time-consuming, operability is not high, inapplicable for the metal material without obvious elastic vertical line segment, it is not suitable for the GB/T228.1 annex J method of successive approximation yet and measures the puller system Cleaning Principle specified in moulding extension strength; 3, R_p0.2Mathematical model be

$R_{p0.2}=\frac{k\×(\mathrm{\Δ}L-0.002\×L_o)}{S}---\left(1\right)$

Wherein, R_p0.2Refer to the plastic elongation intensity (Mpa) that elongation percentage is 0.2%; F_p0.2Refer to the plastic elongation load (N) that elongation percentage is 0.2%; S refers to that specimen cross section amasss (mm²); K refers to that power extends the slope of curve stretch section data linear fit; �� L refers to extend; L_oRefer to extensometer gage length;

Mathematical model is non-linear, exports result R_p0.2Probability distribution be not normal distribution, it is possible to can cause that the uncertainty assessed does not meet reality. Based on above feature, MCM is more suitable for evaluation regulation plastic elongation intensity uncertainty.

There is following defect when evaluating regulation plastic elongation intensity in GUM: (1) needs multiple parallel sample, or needs to take during 100 coordinate points relatively difficult on power-extension curve; (2) R_p0.2Mathematical model non-linear, R_p0.2Probability distribution deviate from normal distribution, when measured value during for measured value with uncertainty evaluation differs bigger, the conversion of the relative uncertainty degree of use causes GUM evaluating precision poor; (3) GUM evaluation is time-consuming longer, is not suitable for each measured value and calculates the uncertainty of himself measured value. (4) slope obtains average and the standard deviation of k by taking 100 matchings on power-extension curve chart, inapplicable on the metal material without obvious elastic vertical line segment, takes a difficulty in such cases, and the slope baseline of matching is poor relative to actual standard can be bigger than normal; (5) determination of the slope baseline non-GB/T228.1 annex J method of successive approximation measures the puller system Cleaning Principle method specified in moulding extension strength. The GB/T228.1 annex J method of successive approximation is applicable to the mensuration with the regulation plastic elongation intensity without obvious elastic vertical line segment metal material. It is more difficult that GUM evaluates uncertainty. The defect of regulation plastic elongation intensity is evaluated for solving above GUM, this method measures with the GB/T228.1 annex J method of successive approximation and specifies that moulding extension strength is for basis, adopt MCM to carry out probability distribution to propagate and calculate uncertainty, use the Mathematica software programming MCM uncertainty evaluation program of WolframResearch company.

Summary of the invention

This invention address that GUM evaluates the defect of the existence of regulation plastic elongation intensity, and measure the moulding extension strength of regulation for basis with the GB/T228.1 annex J method of successive approximation, adopt MCM to carry out probability distribution and propagate calculating uncertainty, it is provided that a kind of regulation plastic elongation intensity uncertainty evaluation method based on Monte Carlo.

The purpose of the present invention is achieved through the following technical solutions: a kind of regulation plastic elongation intensity uncertainty evaluation method based on Monte Carlo, and it comprises the following steps:

S1, set up R_p0.2Mathematical model

$R_{p0.2}=\frac{k\×(\mathrm{\Δ}L-0.002\×L_o)}{S}---\left(1\right)$

Wherein, R_p0.2Refer to the plastic elongation intensity (Mpa) that elongation percentage is 0.2%; F_p0.2Refer to the plastic elongation load (N) that elongation percentage is 0.2%; S refers to that specimen cross section amasss (mm²); K refers to that power extends the slope of curve stretch section data linear fit; �� L refers to extend; L_oRefer to extensometer gage length;

S2, the probability distribution determining the amount of directly inputting according to Given information and parameter

Used standard dynamometer grade to obtain puller system by electronic universal puller system grade and calibration puller system and measure force value probability distribution; The note grade of extending used by test obtains original gauge length is worth probability distribution with extending; Being obtained the probability distribution of dimensional measurements by the slide calliper rule used of measuring of specimen size, specimen cross section amasss S, for sheet coupon

S=La �� Lb----------------------------------------------(2)

Wherein La refers to specimen width (mm); Lb refers to sample thickness (mm);

S3, on a power-extension curve chart, check in (F_p0.2, �� L_p0.2), calculate 0.1F_p0.2��0.5F_p0.2, power-extension curve obtains respectively up and down near 0.1F_p0.2Two pairs of coordinates, up and down near 0.5F_p0.2Two pairs of coordinates, according to the probability distribution Sampling of coordinate figure, by method of least square linear interpolation calculate 0.1F_p0.20.1 �� L_p0.2, calculate 0.5F again by method of least square linear interpolation_p0.20.5 �� L_p0.2, least-squares algorithm linear fitting [{ 0.1F_p0.2, 0.1 �� L_p0.2, { 0.5F_p0.2, 0.5 �� L_p0.2] slope that obtains is elastic deformation baseline k, by [{ 0.1F_p0.2, 0.1 �� L_p0.2, { 0.5F_p0.2, 0.5 �� L_p0.2] probability distribution sampling least square fitting go out a series of k, obtain probability distribution and the parameter of k;

S4, probability distribution PDF according to above-mentioned input quantity carry out �� sampling, for each sample vector, substitute into mathematical model

$R_{p0.2}=\frac{k\×(\mathrm{\Δ}L-0.002\×L_o)}{S}---\left(3\right)$

Corresponding R is calculated with formula (3)_p0.2Model value, and actual tests detection in due to power-extension curve be not desirable smoothed curve, k �� (�� L-0.002 �� L_o) average and the F that checks on power-extension curve chart_p0.2There are differences, probability distribution conversion need to be carried out;

S5, �� R of sequence_p0.2Model value, calculate its average, standard deviation, any probability packet is containing interval.

The invention have the advantages that (1), have only to a tensile sample, and meet power-extension curve chart elastic vertical line segment height and be not less than 0.5F_p0.2Metal material, thus it is limited and can not provide the accurate uncertainty situation of result to meet actual stretching detection sample, this method only need at the coordinate of power-5 points of extension curve acquisition, simple to operate it is greatly saved the uncertainty evaluation time, makes each result provide its accurate uncertainty to be possibly realized; (2), MCM is applicable to the nonlinear mathematical model of regulation plastic elongation intensity; (3), this method adopts the Mathematica software programming MCM uncertainty evaluation program of WolframResearch company, and associate excel file, it is thus achieved that 5 point coordinates only need out of order input excel file directly can show result of calculation at Mathematica software.Make whole evaluation process stability and high efficiency brief. (4), for actual tests detect in due to power-extension curve be not desirable smoothed curve, k �� (�� L-0.002 �� L_o) average and the F that checks on power-extension curve chart_p0.2There are differences, carry out probability distribution conversion and make the uncertainty settled accounts more accurate; (5), this method can obtain uncertainty according to any confidence level (95%, 99% etc.).

Accompanying drawing explanation

Fig. 1 is the computer program flow chart of probability sampling simulation;

Fig. 2 is the structural representation of 6063/T6 aluminum alloy plate materials;

Fig. 3 is the power after Fig. 2 drawn-extension curve chart;

Detailed description of the invention

The present invention is further described below, and protection scope of the present invention is not limited to the following stated:

A kind of regulation plastic elongation intensity uncertainty evaluation method based on Monte Carlo, it comprises the following steps:

S1, set up R_p0.2Mathematical model

$R_{p0.2}=\frac{k\×(\mathrm{\Δ}L-0.002\×L_o)}{S}---\left(1\right)$

Wherein, R_p0.2Refer to the plastic elongation intensity (Mpa) that elongation percentage is 0.2%; F_p0.2Refer to the plastic elongation load (N) that elongation percentage is 0.2%; S refers to that specimen cross section amasss (mm²); K refers to that power extends the slope of curve stretch section data linear fit; �� L refers to extend; L_oRefer to extensometer gage length;

S2, the probability distribution determining the amount of directly inputting according to Given information and parameter

Used standard dynamometer grade to obtain puller system by electronic universal puller system grade and calibration puller system and measure force value probability distribution; The note grade of extending used by test obtains original gauge length is worth probability distribution with extending; Being obtained the probability distribution of dimensional measurements by the slide calliper rule used of measuring of specimen size, specimen cross section amasss S, for sheet coupon

S=La �� Lb------------------------------------------------(2)

Wherein La refers to specimen width (mm); Lb refers to sample thickness (mm);

S3, on a power-extension curve chart, check in (F_p0.2, �� L_p0.2), calculate 0.1F_p0.2��0.5F_p0.2, power-extension curve obtains respectively up and down near 0.1F_p0.2Two pairs of coordinates, up and down near 0.5F_p0.2Two pairs of coordinates, according to the probability distribution Sampling of coordinate figure, by method of least square linear interpolation calculate 0.1F_p0.20.1 �� L_p0.2, calculate 0.5F again by method of least square linear interpolation_p0.20.5 �� L_p0.2, least-squares algorithm linear fitting [{ 0.1F_p0.2, 0.1 �� L_p0.2, { 0.5F_p0.2, 0.5 �� L_p0.2] slope that obtains is elastic deformation baseline k, by [{ 0.1F_p0.2, 0.1 �� L_p0.2, { 0.5F_p0.2, 0.5 �� L_p0.2] probability distribution sampling least square fitting go out a series of k, obtain probability distribution and the parameter of k;

S4, probability distribution PDF according to above-mentioned input quantity carry out �� sampling, for each sample vector, substitute into mathematical model

$R_{p0.2}=\frac{k\×(\mathrm{\Δ}L-0.002\×L_o)}{S}---\left(3\right)$

Calculate corresponding R_p0.2Model value, and actual tests detection in due to power-extension curve be not desirable smoothed curve, k �� (�� L-0.002 �� L_o) average and the F that checks on power-extension curve chart_p0.2There are differences, probability distribution conversion need to be carried out;

S5, �� R of sequence_p0.2Model value, calculate its average, standard deviation, any probability packet is containing interval.

Embodiment one: with 6063/T6 aluminum alloy plate materials sample as in figure 2 it is shown, width La=12.5, thickness Lb=2.56, test platform is for thinking carefully safe prompt microcomputer controlled electronic universal tester, model: CMT5504, maximum pull 50KN, accuracy class 0.5 grade. Verifier calibration dynamometer grade used is 0.3 grade, takes k=2, and error is 0.3%/2. Electronic digital indicator (specification: 0��200mm), the error of indication �� 0.01mm.Extensometer gage length 50mm, gauge length relative error 0.5%, extensometer measures relative error 0.5%. Tensile strain rate is 0.00025/s.

Power-extension curve chart is obtained after being detected by 6063/T6 aluminum alloy plate materials sample drawn in Fig. 1, as it is shown on figure 3, F in Fig. 3_p0.2Point coordinates 0.278,7958.268N}, up and down near 0.1F_p0.2(795.8268N) two point coordinates respectively [{ 0.0134625,793.755N}, { 0.013595,801.880N}]; Up and down near 0.5F_p0.2(3979.134N) two point coordinates respectively [{ 0.0836725,3945.255N}, { 0.0859975,4046.265N}].

2, the probability distribution of component is inputted

(1) universal tensile testing machine load distribution, puller system grade is 0.5 grade, and relative error �� 0.5% is set to be uniformly distributed, F_p0.2* U [1-0.5%, 1+0.5%];

(2) verifier calibration dynamometer grade used is 0.3 grade, takes k=2, and relative error is �� 0.3%/2, is set to be uniformly distributed, F_p0.2* U [1-0.15%/2,1+0.15%/2];

(3) the original gauge length 50mm of extensometer, gauge length relative error is 0.5%, is set to be uniformly distributed, L₀* U [1-0.5%, 1+0.5%];

(4) extensometer measures relative error �� 0.5%, is set to be uniformly distributed, �� L*U [1-0.5%, 1+0.5%];

(5) original cross-sectional area S partial uncertainty has the error of indication �� 0.01 (set and be uniformly distributed) of slide gauge, and repetition measurement error (sets normal distribution). Width La=12.5+N [0,0.01]+U [-0.01,0.01], thickness: Lb=2.1+N [0,0.01]+U [-0.01,0.01];

(6) deterministic force-extension slope of curve k, F_p0.2Point coordinates 0.278,7958.268N}, up and down near 0.1F_p0.2(795.8268N) two point coordinates [{ 0.0134625,793.755N}, { 0.013595,801.880N}], up and down near 0.5F_p0.2(3979.134N) 2 points [{ 0.0836725,3945.255N}, { 0.0859975,4046.265N}].

, then the coordinate probability distribution of every is:

[��L_i* U [1-0.5%, 1+0.5%], F_i* U [1-0.5%, 1+0.5%] * U [1-0.15%/2,1+0.15%/2]], use linear interpolation to obtain 0.1F_p0.2, 0.5F_p0.2Extend coordinate;

(7) according to 0.1F_p0.2, 0.5F_p0.2Coordinate linear least squares fit goes out slope baseline k, it is thus achieved that the probability distribution of k;

(8) according to above-mentioned R_p0.2Mathematical model, calculate R_p0.2Probability distribution, seek R_p0.2Average, standard deviation, the probability interval of 95%, the probability interval of 99%, Composite Seismogram.

Mathematica is used to realize following code:

Claims (1)

1. the regulation plastic elongation intensity uncertainty evaluation method based on Monte Carlo, it is characterised in that: it comprises the following steps:

S1, set up R_p0.2Mathematical model

$R_{p0.2}=\frac{k\×\left(\mathrm{\Δ}L-0.002\×L_o\right)}{S}---\left(1\right)$

Wherein, R_p0.2Refer to the plastic elongation intensity (Mpa) that elongation percentage is 0.2%; F_p0.2Refer to the plastic elongation load (N) that elongation percentage is 0.2%; S refers to that specimen cross section amasss (mm²); K refers to that power extends the slope of curve stretch section data linear fit; �� L refers to extend; L_oRefer to extensometer gage length;

S2, the probability distribution determining the amount of directly inputting according to Given information and parameter

Used standard dynamometer grade to obtain puller system by electronic universal puller system grade and calibration puller system and measure force value probability distribution; The note grade of extending used by test obtains original gauge length is worth probability distribution with extending; Being obtained the probability distribution of dimensional measurements by the slide calliper rule used of measuring of specimen size, specimen cross section amasss S, for sheet coupon

S=La �� Lb------------------------------------------------(2)

Wherein La refers to specimen width (mm);Lb refers to sample thickness (mm);

S3, on a power-extension curve chart, check in (F_p0.2, �� L_p0.2), calculate 0.1F_p0.2��0.5F_p0.2, power-extension curve obtains respectively up and down near 0.1F_p0.2Two pairs of coordinates, up and down near 0.5F_p0.2Two pairs of coordinates, according to the probability distribution Sampling of coordinate figure, by method of least square linear interpolation calculate 0.1F_p0.20.1 �� L_p0.2, calculate 0.5F again by method of least square linear interpolation_p0.20.5 �� L_p0.2, least-squares algorithm linear fitting [{ 0.1F_p0.2, 0.1 �� L_p0.2, { 0.5F_p0.2, 0.5 �� L_p0.2]] slope that obtains is elastic deformation baseline k, by [{ 0.1F_p0.2, 0.1 �� L_p0.2, { 0.5F_p0.2, 0.5 �� L_p0.2] probability distribution sampling least square fitting go out a series of k, obtain probability distribution and the parameter of k;

S4, probability distribution PDF according to above-mentioned input quantity carry out �� sampling, for each sample vector, substitute into mathematical model $R_{p0.2}=\frac{k\×\left(\mathrm{\Δ}L-0.002\×L_o\right)}{S}---\left(3\right)$

Corresponding R is calculated with formula (3)_p0.2Model value, and actual tests detection in due to power-extension curve be not desirable smoothed curve, k �� (�� L-0.002 �� L_o) average and the F that checks on power-extension curve chart_p0.2There are differences, probability distribution conversion need to be carried out;

S5, �� R of sequence_p0.2Model value, calculate its average, standard deviation, any probability packet is containing interval.