CN105716946A - Measuring method for predicting uniaxial constitutive relation of material by pressing cylindrical flat head in material - Google Patents

Abstract

The invention discloses a measuring method for predicting a uniaxial constitutive relation of a material by pressing a cylindrical flat head in the material. The measuring method comprises the following steps: carrying out quasi-static pressing-in loading on the smooth surface of the material by using the hard alloy cylindrical flat and straight pressure head; after obtaining a continuous load P-depth h curve, simply processing through a load-displacement curve to obtain elastic pressing-in rigidity S, elastic-plastic loading curvature C and loading index m; and carrying out post processing on the uniaxial constitutive relation of the predicted material. By the measuring method, the shortcomings that by an existing cylindrical pressing-in technology, only elasticity modulus E and yield strength oy of the material can be approximately estimated, a hardening law of the material is difficult to obtain and the like are overcome, the uniaxial constitutive relation of the material can be effectively predicted simply and conveniently, and the measuring method is suitable for testing performances of light materials, soft materials and the like. The measuring method is good in testing effect, has universality, and therefore can be used for analyzing the constitutive relation of the material and multifactorial mechanical effects under the complex loading conditions of creepage, impact and the like. Particularly, the measuring method is of great significance to acquisition of uniaxial mechanical properties of light materials widely used in transportation engineering such as aerospace, high-speed rails, ships, automobiles and the like, biomedical engineering soft materials and the like.

Description

The assay method of cylindrical tack press-in prediction material single shaft constitutive relation

Technical field

The present invention relates to material mechanical performance test new theory and new method, the most in-service advanced engineering structure The field tests of light material single shaft constitutive relation.

Background technology

Simple stress-strain curve (i.e. constitutive relation) is the key link of material and mechanics opening relationships, right Safe design and military service in engineering component play an important role.Obtain the usual of material single shaft constitutive relation Way is to choose raw material processing or stretch at laboratory after intercepting standard tensile specimen from engineering component Test.Along with miniaturization and the lightweight of engineering structure development, limited by component yardstick, it is difficult to according to tradition Sampling method obtain effectively sample launch test.But, for in-service aviation, high ferro, boats and ships, vapour The lightweight structural material that the Transportation Engineerings such as car are widely present, uses tradition stretching test method when intercepting sample Certainly will destroy its service state, the cylindrical press-in test with features such as original position, micro-damages then can meet Demand.Additionally, for expensive brand-new material (such as nano-particle reinforcement material, specific function coating Material etc.) and tradition precious metal material (such as magnesium alloy, titanium alloy etc.), use tradition tension test side Method cost is high, easily cause bigger waste of material and reclaim energy consumption greatly, the problem such as not environmentally.For above-mentioned feelings Condition, the most still lacks what convenient, effective and stable method was predicted for material or structure single shaft constitutive relation Detection technique.

Cylindrical tack indentation test is a kind of test method being usually used in the acquisition of material creep performance^[3], but less It is used to test the single shaft mechanical property of material.It is true that cylindrical tack indentation test process can be analogous to Local Axial compression tests with periphery material constraint.Although the deformable material under this load mode is residing should Power state is unsatisfactory for simple single shaft (compression) stress state, but its load-deflection behavior contains enough and Highly effective material elastic plastic mechanical properties characterization information, by carrying out technology wound to this existing test method Newly, the simple and effective measurement of material single shaft constitutive relation can be realized.

Prior art

2013-2015, Hu Zhong etc.^[4,5]Based on micro-nano cylindrical tack indentation test, by continuously Gather the load p-degree of depth h curve in indentation test loading procedure, it is proposed that based on hemi-spherical cavities model with have The Approximate prediction formula of limit unit simulation.This technical scheme is estimated the elastic modulus E of material by formula (1) and bends Take intensity σ_y。

$\left\{\begin{array}{cc}P\≈1.72A\frac{h}{a}{c}_0(v,\mathrm{\μ})E& P\≤P_e\\ P\≈{\mathrm{kA\σ}}_y& P/P_e=0.839\end{array}\right.---\left(1\right)$

Wherein, A is cylindrical crimp cross-sectional area, A=π D²/ 4, D are the column indenter indentation diameter, and E is elastic modelling quantity, σ_yFor yield stress, a is contact radius, c₀For the coefficient relevant with coefficientoffrictionμ and Poisson's ratio ν, k is for needing The correction factor of Experimental Calibration, k=[2/3+2ln (c/a)], P_eFor elastic limit load.

In prior art, approximate formula based on hemi-spherical cavities model with finite element modelling can only be estimated Elastic modulus E and yield strength σ_y, it is impossible to the prediction Hardening Law of material thus can not get continuous print stress-strain Curve；Secondly, the method also needs to unloading after indentation test loads, effectively measuring often to reality of unloading The required precision testing equipment and sample surfaces process is higher；Further, when obtaining yield strength, need to use Experimental Calibration goes out suitable k, there is the trouble of debugging；Additionally, the approximate formula yield load definition of the method Three kinds of material proximates in literary composition are met by P/Pe=0.839, but whether possess universality and understand not yet.

List of references:

[1]Hollomon J H.Tensile deformation[J].AIME TRANS,1945,12(4):1-22.

[2]Cao Y P,Qian X Q,Lu J,et al.An energy-based method to extract plastic properties of metal materials from conical indentation tests[J].Journal of materials research,2005,20(05): 1194-1206.

[3] Yue Zhufeng. Cylindrical indentation measuring technology and application [M] thereof. Beijing: Science Press, 2010.

[4]Hu Z,Lynne K,Delfanian F.Characterization of materials'elasticity and yield strength through micro-/nano-indentation testing with a cylindrical flat-tip indenter[J].Journal of Materials Research, 2015,30(04):578-591.

[5]Hu Z,Lynne K J,Markondapatnaikuni S P,et al.Material elastic–plastic property characterization by nanoindentation testing coupled with computer modeling[J].Materials Science and Engineering:A,2013,587:268-282.

Summary of the invention

It is an object of the invention to provide a kind of based on the theoretical only consideration press-in section of P-h curve, the method for equivalent energy The easiest cylindrical tack indentation test technical scheme, easy can realize having of material single shaft constitutive relation Effect is measured.

Goal of the invention is to be realized in that cylindrical tack press-in prediction material single shaft constitutive relation Assay method, use hard alloy cylinder bright and clean material surface is carried out quasistatic press-in load, it is thus achieved that Calibrating elastic press-in rigidity S respectively by loading-depth curve after continuous print load p-press deep h curve, bullet is moulded Property load curvature C and load exponent m, postmenstruation process prediction material single shaft constitutive relation；Later stage process comprises Following steps:

1) according to formula (1), cylindrical tack press-in is divided into linear elasticity section and elastoplasticity section, uses linear trend Line returns P-h curve stretch section and obtains elastic press-in rigidity S, uses power law Trendline to return P-h curve bullet Plasticity section obtains elastoplasticity and loads curvature C and load exponent m；

2) by 1) acquired results input (2) formula

$\left\{\begin{array}{c}S=ED/(1-v^2)\\ C=v^{*}{k}_1{k}_3^n(m+1)D^{2-m}\\ m=k_{4}n+k_2\end{array}\right.---\left(2\right)$

Measurable go out measured material or constitutive parameter E, σ of component_y、n.In formula: S is load p-degree of depth h curve The slope (i.e. elastic press-in rigidity) of initial line stretch section, E is the elastic modelling quantity of material, and v is material pool Pine ratio, v^*It is characterized energy density and meets v^*=Eⁿσ_y ^1-n/ (1+n), n are strain hardening exponent, σ_yRun after fame Justice yield strength, D is cylindrical crimp diameter of section, and C is for loading curvature, and m is for loading index, k₁、 k₂、k₃With k₄Constant is solved for nondimensional；

3) by 2) obtain E, σ_y, n result input following Hollomon model

$\mathrm{\σ}=\left\{\begin{array}{cc}E\mathrm{\ϵ}& \mathrm{\σ}\≤{\mathrm{\σ}}_y\\ E^n{\mathrm{\σ}}_y^{1-n}{\mathrm{\ϵ}}^n& \mathrm{\σ}\≥{\mathrm{\σ}}_y\end{array}\right.---\left(3\right)$

Material single shaft constitutive relation can be obtained.Hollomon model^[1,2]It is considered to effectively describe a large amount of engineering solid Simple stress-the strain stress relation of body material.

The method of the present invention overcomes existing cylindrical pressing-in technology and adjusts based on empirical equation and loaded down with trivial details parameter Elasticity modulus of materials E and yield strength σ are estimated in examination_y, it is impossible to the prediction Hardening Law of material thus can not get The defects such as continuous print load-deformation curve, can realize material single shaft constitutive relation simple and effectively and obtain, effect Fruit is preferable.Especially in the Transportation Engineerings such as Aero-Space, high ferro, boats and ships, automobile widely used gently Material single shaft mechanical property obtains significant.Formula (1) also can help for creep, impact The mechanics effect analysis (such as analysis of Residual Stress) of material constitutive relation and correlative factor is carried out etc. loading environment.

Accompanying drawing explanation

Fig. 1 is the assay device schematic diagram that the present invention uses.

Fig. 2 typically cylindrical loading of pressing in displacement curve figure.

Fig. 3 5083-H112 aluminum alloy round cylindricality loading of pressing in-depth curve figure.

Fig. 4 5083-H112 aluminium alloy single shaft this structure curve prediction result figure.

Fig. 5 cylinder press-in finite element analysis three-dimensional model diagram.

Fig. 6 is the parameter value table in formula (3) formula (3).

Detailed description of the invention

Below in conjunction with the accompanying drawings the inventive method is described in further detail.

The technical solution adopted in the present invention includes two parts: cylindrical tack indentation test, cylinder are flat Head press-in equivalent energy theory-FEM (finite element) model.

(1) cylindrical tack indentation test

Obtained accurate and abundant load p by cylindrical tack indentation test～degree of depth h test data is skill of the present invention The most important condition of art scheme, in order to ensure to avoid pressure head to deform while obtaining enough material deformation informations Impact on result of the test, for general macroscopic view press-in, compression distance selects 50～100 μm.Now, Polish after need to carrying out abrasive paper for metallograph polishing for material to be measured or body structure surface, make surface roughness Ra be less than Just can carry out quasi static indentation after 0.32 μm, device is as shown in Figure 1.As need to be to nanoscale or bigger chi Degree material is tested, as long as material is relatively uniform, the degree of depth or load test are it is achieved that then compression distance Do not limit.

(2) the equivalent energy theory-FEM (finite element) model of cylindrical tack press-in

Fig. 2 gives typical cylindrical tack indentation test load p～degree of depth h relation, and has marked two and add Some basic physical parameters in load stage.

Theoretical derivation and finite element numerical simulation show that any physical dimension cylindrical crimp is at different compression distances Under elastic press-in rigidity S, elastoplasticity loads curvature C and loads exponent m with material constitutive parameter (E, σ_y、n) Between meet following relation:

$\left\{\begin{array}{c}S=ED/(1-v^2)\\ C=v^{*}{k}_1{k}_3^n(m+1)D^{2-m}\\ m=k_{4}n+k_2\end{array}\right.---\left(1\right)$

In formula: S is the slope (i.e. elastic press-in rigidity) of load p-degree of depth h curve initial linear elasticity section, and E is The elastic modelling quantity of material, v is material Poisson's ratio, v^*It is characterized energy density and meets v^*=Eⁿσ_y ^1-n/ (1+n), N is strain hardening exponent, σ_yFor nominal-ultimate strength, D is cylindrical crimp diameter of section, and C is for loading Curvature, m is for loading index, k₁、k₂、k₃With k₄For the nondimensional constant that solves, and parameter value scope As shown in Figure 6；

The simple stress of most of light-weight metals and alloy (such as aluminium alloy, magnesium alloy, titanium alloy etc.) thereof-should Change relation all meets good Hollomon power law hardening model^[4], the most satisfied

$\mathrm{\σ}=\left\{\begin{array}{cc}E\mathrm{\ϵ}& \mathrm{\σ}\≤{\mathrm{\σ}}_y\\ E^n{\mathrm{\σ}}_y^{1-n}{\mathrm{\ϵ}}^n& \mathrm{\σ}\≥{\mathrm{\σ}}_y\end{array}\right.---\left(2\right)$

In formula, E is elastic modelling quantity, σ_yFor nominal yield stress, n is strain hardening exponent.

In technical solution of the present invention, any physical dimension hard alloy cylindrical crimp can be used material list Face carries out quasistatic press-in and loads, thus obtains continuous print load p-degree of depth h curve.Pass through loading-depth curve Linear elasticity segment data can calibrate elastic press-in rigidity S, return can obtain by elastoplasticity segment data power law Elastoplasticity loads curvature C and loads exponent m, substitute into formula (1) and measured material or component can be doped Constitutive parameter E, σ_y, n, and then determined its single shaft constitutive relation by formula (2).

Embodiment

In technical solution of the present invention, the present invention is based on equivalent energy theoretical derivation and simple finite element meter several times Calculate and propose the innovative technology theoretical system using cylindrical tack press-in prediction material single shaft constitutive relation.

Use the hard alloy cylindrical crimp of a diameter of 2mm to 5083-H112 aluminum alloy sample (cylindrical, High 10mm × diameter 10mm) carry out indentation test and ask for its single shaft constitutive relation curve.Fig. 4 is given Load p-degree of depth h curve that 5083-H112 aluminium alloy obtains under cylinder press-in loads.Data process Flow process is: first loading of pressing in P-degree of depth h curve carries out zero point translation, more bent by loading of pressing in-degree of depth In line, taking-up initial line stretch section data carry out linear regression and obtain elastic press-in rigidity S, can be by formula (1) Converse the elastic modulus E of material.Then, take out the data in elastic-plastic deformation stage to return according to power law To loading curvature C and loading exponent m, substitute into formula (1) and try to achieve plastic σ_y, n, finally by formula (2) Determine the single shaft constitutive relation of 5083-H112 aluminum alloy sample.Fig. 4 is technical solution of the present invention prediction 5083-H112 aluminium alloy single shaft constitutive relation curve is with the ratio of this structure curve obtained by tradition tension test Relatively.

Claims (1)

1. the assay method of cylindrical tack press-in prediction material single shaft constitutive relation, uses hard alloy cylinder Bright and clean material surface carries out quasistatic press-in load, it is thus achieved that by carrying after the deep h curve of continuous print load p-press Lotus-depth curve calibrates elastic press-in rigidity S respectively, and elastoplasticity loads curvature C and loads exponent m, Process prediction material single shaft constitutive relation postmenstruation；Later stage process comprises the steps of:

1) according to formula (1), cylindrical tack press-in is divided into linear elasticity section and elastoplasticity section, uses linear trend Line returns P-h curve stretch section and obtains elastic press-in rigidity S, uses power law Trendline to return P-h curve bullet Plasticity section obtains elastoplasticity and loads curvature C and load exponent m；

2) by 1) acquired results input (2) formula

$\left\{\begin{array}{c}S=ED/(1-v^2)\\ C=v^{*}{k}_1{k}_3^n(m+1)D^{2-m}\\ m=k_{4}n+k_2\end{array}\right.---\left(2\right)$

Measurable go out measured material or constitutive parameter E, σ of component_y, n, in formula: S is load p-degree of depth h curve The slope of initial line stretch section, E is the elastic modelling quantity of material, and v is material Poisson's ratio, v^*It is characterized energy Density and meet v^*=Eⁿσy^1-n/ (1+n), n are strain hardening exponent, σ_yFor nominal-ultimate strength, D is circle Cylindricality pressure head diameter of section, C is for loading curvature, and m is for loading index, k₁、k₂、k₃With k₄For dimensionless Solve constant；

3) by 2) obtain E, σ_y, n result input following Hollomon model

$\mathrm{\σ}=\left\{\begin{array}{cc}E\mathrm{\ϵ}& \mathrm{\σ}\≤{\mathrm{\σ}}_y\\ E^n{\mathrm{\σ}}_y^{1-n}{\mathrm{\ϵ}}^n& \mathrm{\σ}\≥{\mathrm{\σ}}_y\end{array}\right.---\left(3\right)$

Material single shaft constitutive relation can be obtained.