CN106248502A - The method that cantilever beam bending obtains material elastic plastic mechanical properties - Google Patents

Abstract

The invention discloses the method that the bending of a kind of cantilever beam obtains material elastic plastic mechanical properties, use hard alloy cylinder Kun that cantilever beam free end is carried out quasistatic vertically to load, linear rigidity S is obtained by this curve after obtaining continuous print load p amount of deflection h curve, load curvature C and load exponent m, predicting material elastic plastic mechanical properties parameter through simple process.The present invention overcomes existing cantilever beam measuring technology and rely on empirical equation, it is impossible to obtain the defects such as hardened material rule.The structural material single shaft mechanical properties such as membranaceous, the tabular that the present invention is widely present for key projects such as MEMS, optical engineering, Communication Engineering, biomedical engineerings obtain significant.

Description

The method that cantilever beam bending obtains material elastic plastic mechanical properties

Technical field

The present invention relates to material mechanical performance test, the membrane structure material single shaft mechanics being especially widely present in engineering The field tests of performance.

Background technology

The basic mechanical performance of material such as modulus, intensity and hardening parameter all can be as the bases of material structure safety evaluation This condition, analyzes significant to engineering safety.

Along with developing rapidly of miniaturized structure, especially it is widely used in optical engineering with small-scale structures such as thin film, communication The new scientific and trechnolocial undertaking such as technology and biomedical engineering, therefore its Mechanics Performance Testing gradually causes the concern of researcher.Adopt When this membranelike structure being tested with tradition stretching, there is clamping, to medium many difficulties, it is difficult to the essence of guarantee test result Degree.Further, for expensive function film, use tradition stretching test method to be difficult to prepare standard specimen, and be difficult to disappear Except problems such as bias-loads.For above-mentioned situation, the most still lack easy and simple to handle and good with repeatability for material or knot The easy detection technology of structure single shaft constitutive relation prediction.

Micro-cantilever bend test is a kind of in the last thirty years for the method for thin film material mechanics performance test, but more Research concentrates on scale effect and the strain gradient plasticity of material^[1].The press-in of taper in recent years is gradually used to test the list of material Axle elastic plastic mechanical properties.It is true that taper loading of pressing in-depth relationship is the important body of measured material elastic plastic mechanical properties Existing, by this existing test method is carried out theory and technology innovation, the easy measurement of material single shaft constitutive relation can be realized.

Prior art 1

Nix et al.^[3]The mechanical property of gold film initially with micro-cantilever crooked test technical limit spacing.According to outstanding Arm beam bending elasticity theory proposes following simple appraising model:

$\left\{\begin{array}{c}h=4{\mathrm{Pc}}^3(1-v^2)/\left({\mathrm{bt}}^{3}E\right)\\ {\mathrm{\σ}}_y=6{\mathrm{cP}}_y/{\mathrm{bt}}^2\end{array}\right.---\left(1\right)$

Wherein h is load(ing) point amount of deflection, and P is concentrfated load, and c is the effective length of beam, b, t be respectively beam section width and Thickness, E and v is respectively elastic modelling quantity and the Poisson's ratio of material, σ_yFor the yield stress of material, P_yFor yield load.This technical side Case is mainly by elastic modulus E formula (1) obtained and yield stress σ_y。

Prior art 2

Trueba etc.^[4]Indirectly obtain based on repeatedly FEM calculation and the mode that the test of micro-beam deflection combines in situ The elastic modelling quantity of WC Co material and fracture strength.Its substantially process can be described as: uses spheroidal pressure head micro-to in-service WC Co Beam carries out Quasistatic Bending test, until micro-beam ruptures, records continuous print load p-amount of deflection h curve during this；Borrow Helping ABAQUS finite element software to adjust input material performance parameter makes result close with test, material during final output convergence Parameter is test value.

In prior art 1, ductile material plastoelasticity behavior approximation is used elastic deflection theory Approximate prediction Elastic parameter E and plasticity parameter yield strength σ near elastic stage_yThere is certain practicality, but obvious to hardening Material is then difficult to ensure that the continuation Temperature measurement after precision of prediction, and the unpredictable material yield of the method.

In prior art 2, needing loaded down with trivial details finite element iterative to calculate process, the convergence of iteration has initial value and relies on Property, lacking effective theory support, testing equipment requires height, and final giving solves and application causes inconvenience.

List of references:

[1]Motz C,T,Pippan R.Mechanical properties of micro-sized copper bending beams machined by the focused ion beam technique[J].Acta Materialia,2005,53(15):4269-4279.

[2]Gao H,Huang Y,Nix W D,et al.Mechanism-based strain gradient plasticity—I.Theory[J].Journal of the Mechanics and Physics of Solids,1999, 47(6):1239-1263.

[3]Weihs T P,Hong S,Bravman J C,et al.Mechanical deflection of cantilever microbeams:A new technique for testing the mechanical properties of thin films[J].Journal of Materials Research,1988,3(05):931-942.

[4]Trueba M,Aramburu A,Rodríguez N,et al.“In-situ”mechanical characterisation of WC–Co hardmetals using microbeam testing[J].International Journal of Refractory Metals and Hard Materials,2014,43:236-240.

Summary of the invention

It is an object of the invention to provide a kind of, cantilever beam bend test that method the easiest theoretical based on equivalent energy Technical scheme, to realize the easy acquisition of material single shaft Elastoplastic Performances in Simulation.

The means realizing goal of the invention are: the method that the bending of a kind of cantilever beam obtains material elastic plastic mechanical properties, use Hard alloy cylinder Kun carries out single Quasistatic Bending load test to square-section cantilever beam, it is thus achieved that continuous print load p-scratch Degree h curve, is then processed by simple data and can obtain material elastic plastic mechanical properties；Its detailed process includes:

1) cantilever beam BENDING LOAD-DEFLECTION CURVES IN meets the rule shown in formula (1), uses power law to return P-h curve and adds Carry section and obtain its loading curvature C；

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

$\left\{\begin{array}{c}S=3EI/L^3\\ C=v^{*}{k}_1{k}_3^n(m+1)A^{*}{h}^{*-m}\\ m=k_{4}n+k_2\end{array}\right.---\left(2\right)$

Measurable go out measured material or constitutive parameter E, σ of component_y, n, in formula: S be the elastic bending rigidity of material (i.e. The slope of load-amount of deflection linear elasticity section), E is the elastic modelling quantity of material, and v is material Poisson's ratio, v^*It is characterized energy density and expires Foot v^*=Eⁿσ_y ^1-n/ (1+n), n are strain hardening exponent, σ_yFor nominal-ultimate strength, L is the length of beam, and I is cross sectional moment of inertia And I=BH²/ 12, B are beam section width, and H is beam section height, and D is the cross-sectional diameter loading Kun, and C is for loading curvature, and m is Load index.

3) according to 2) σ that obtains_y, n result, substitute into formula:

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

The single shaft constitutive relation of measured material can be obtained.

Further, described nondimensional constant k is solved₁、k₂、k₃、k₄FEA calibration value be respectively 2.604,0.06, 0.5121 and 1.

The method of the present invention overcomes the unpredictable Temperature measurement of prior art and substantial amounts of FEM calculation, loaded down with trivial details changing For defects such as solution procedure and reverse stability are difficult to ensure that, obtaining of material elastic plastic mechanical properties can be realized simple and effectively Take, satisfactory for result and there is universality, it is adaptable to from micro-meter scale until macroscopic view millimeter, the material press-in test of centimeter scale. The function being widely present especially for key projects such as MEMS, optical engineering, Communication Engineering, biomedical engineerings is thin Film, the material elastic plastic mechanical properties of thin-slab structure obtain significant.Formula (1) also can be by for creep, impact The mechanics effect analysis of material constitutive relation and correlative factor is carried out etc. loading environment.

Accompanying drawing explanation

Fig. 1 is that the cantilever beam bending that the present invention uses loads schematic diagram.

Fig. 2 is the three-dimensional model diagram of charger

Fig. 3 is typical cantilever beam BENDING LOAD-DEFLECTION CURVES IN figure.

Fig. 4 is aluminium foil cantilever beam BENDING LOAD-DEFLECTION CURVES IN figure.

Fig. 5 is that aluminium foil cantilever beam bending simple stress-strain curve predicts the outcome figure.

Fig. 6 is that aluminium foil cantilever beam bends finite element analysis model figure.

Fig. 7 is the parameter value table in formula (2).

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: micro-beam deflection is tested, micro-beam deflection Energy Equivalent is theoretical Model.

(1) micro-beam deflection test

The pass spline that load p～amount of deflection h trial curve accurately are technical solution of the present invention is obtained by the test of micro-beam deflection Part.For conventional micro-beam deflection test, in order to obtain enough material deformation informations, load deflection should keep certain with beam length Proportion is to be advisable not less than 0.2.Assay device is as shown in Figure 1.If nanoscale or more large scale material need to be surveyed Examination, as long as material meets relatively uniform, amount of deflection or load test it is achieved that then amount of deflection size do not limit.

(2) micro-beam deflection Energy Equivalent theoretical model

Fig. 2 gives typical cantilever beam bend test load p～amount of deflection h relation, and identifies load phase and be divided into line Elastic stage and elastic-plastic phase.Theoretical derivation and finite element numerical simulation show loading coefficient C and load the most same material of exponent m Material constitutive parameter E, σ_y, n meet following relation:

$\left\{\begin{array}{c}S=3EI/l^3\\ C=v^{*}{k}_1{k}_3^n(m+1)A^{*}{h}^{*-m}\\ m=k_{4}n+k_2\end{array}\right.---\left(3\right)$

In formula: S is the slope (elastic bending rigidity) of the load-amount of deflection linear elasticity section of material, and E is the springform of material Amount, v is material Poisson's 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, L is the length of beam, and I is cross sectional moment of inertia and I=BH²/ 12, B are beam section width, and H is beam section height, D For the diameter of cylindrical Kun, C is for loading curvature, and m is for loading index, k₁、k₂、k₃With k₄For the nondimensional constant that solves, and constant Value as shown in Figure 7；

Its occurrence is listed in Fig. 7.

In technical solution of the present invention, can use cylinder Kun that cantilever beam free end is carried out Quasistatic Bending loading, thus Obtain continuous print load p-amount of deflection h curve.By load-deflection curve loaded segment data can calibrate elastic bending rigidity S, Load curvature C and loading exponent m substitutes into formula (3) and can dope single shaft constitutive parameter E, σ of measured material_y, n, and then by formula (2) its single shaft constitutive relation is determined.

Embodiment

In technical solution of the present invention, demarcate based on energy equivalence Principle and a small amount of Parameters of Finite Element and propose employing cantilever Beam deflection obtains the technical know-how new system of material elastic plastic mechanical properties.

Cylindrical hard alloy Kun beam micro-to aluminium foil (length to height ratio is L:H=1.5:1) is used to carry out Quasistatic Bending test And ask for its simple stress-strain curve.Fig. 4 give micro-cantilever bend test obtain the load under unit width- Sag curve.Data handling procedure is: first according to linear elasticity section matching, bend test load-deflection curve is carried out zero point and repaiies Just, then recurrence obtains elastic bending rigidity S；Then its non-linear section of matching (elastoplasticity) obtains loading curvature C and loading refers to Number m.Finally S, C and m of obtaining are substituted into formula (1) and try to achieve constitutive parameter σ_y, n, finally determined T225NG titanium alloy by formula (2) Single shaft constitutive relation.Fig. 5 is that the T225NG titanium alloy single shaft constitutive relation curve of technical solution of the present invention prediction draws with by tradition Stretch the comparison of the constitutive relation curve that test obtains.

Claims (2)

1. the method that cantilever beam bending obtains material elastic plastic mechanical properties, uses hard alloy cylinder Kun to cut rectangle Face cantilever beam carries out single Quasistatic Bending load test, it is thus achieved that continuous print load p-amount of deflection h curve, then by simple number Material elastic plastic mechanical properties is obtained according to processing；Its detailed process includes:

1) cantilever beam bend test curve meets the rule shown in formula (1), uses power law to return P-h curve loaded segment and obtains it Load curvature C；

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

$\left\{\begin{array}{c}S=3EI/L^3\\ C=v^{*}{k}_1{k}_3^n(m+1)A^{*}{h}^{*-m}\\ m=k_{4}n+k_2\end{array}\right.---\left(2\right)$

Measurable go out measured material or constitutive parameter E, σ of component_y, n, in formula: S is load p-amount of deflection h curve initial linear elasticity section Slope, E is the elastic modelling quantity of material, and 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 Kun diameter, and L is the length of beam, and I is cross sectional moment of inertia and I =BH²/ 12, B are beam section width, and H is beam section height, and C is for loading curvature, and m is for loading index, k₁、k₂、k₃With k₄For immeasurable Guiding principle solve constant；

3) according to 2) σ that obtains_y, n result, substitute into formula:

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

Obtain the single shaft constitutive relation of measured material.

The method that cantilever beam the most according to claim 1 bending obtains material elastic plastic mechanical properties, it is characterised in that Described during length to height ratio L:H=1.5:1 nondimensional solve constant k₁、k₂、k₃、k₄FEA (finite element analysis) calibration value be respectively 2.604,0.06,0.5121 and 1；For other length to height ratios, only need to simply re-scale k in finite element₁、k₂、k₃、k₄, we Described in method, model stands good.