CN105865915A - Soft material mechanical performance measurement apparatus and method thereof - Google Patents

Soft material mechanical performance measurement apparatus and method thereof Download PDF

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Publication number
CN105865915A
CN105865915A CN201610225141.2A CN201610225141A CN105865915A CN 105865915 A CN105865915 A CN 105865915A CN 201610225141 A CN201610225141 A CN 201610225141A CN 105865915 A CN105865915 A CN 105865915A
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soft material
voice coil
coil motor
computer
main shaft
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CN105865915B (en
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朱福龙
陶加全
潘永军
蔺欣欣
何黎平
段科
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Huazhong University of Science and Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/16Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
    • G01B11/165Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge by means of a grating deformed by the object
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/32Investigating strength properties of solid materials by application of mechanical stress by applying repeated or pulsating forces
    • G01N3/38Investigating strength properties of solid materials by application of mechanical stress by applying repeated or pulsating forces generated by electromagnetic means

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Electromagnetism (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)

Abstract

The invention discloses a soft material mechanical performance measurement apparatus and a method thereof. The apparatus comprises a voice coil motor, a controller, a computer, a translation stage and a CCD camera, the voice coil motor is arranged on a rack and is controlled by the controller, the voice coil motor comprises a grid ruler, a force sensor and a main shaft which are arranged in the voice coil motor, the controller is connected with the computer, and the controller drives the voice coil motor to linearly move along a vertical direction according to an instruction sent by the computer, and sends the displacement and load data obtained by the grid ruler and the force sensor to the computer in order to obtain the load-displacement relationship of a soft material to be measured; and the translation stage is arranged under the voice coil motor and is used for disposing the soft material, one side of the soft material is provided with the CCD camera, and the CCD camera is used for shooting the deformation image of the soft material before and after pressurization and transmitting the deformation image to the computer. The method uses the measurement apparatus to measure. The apparatus and the method have the advantages of compact structure, complete functions, high measurement precision and wide measurement range.

Description

A kind of soft material mechanical property measuring device and method
Technical field
The invention belongs to soft material Mechanics Performance Testing field, more particularly, to a kind of soft material power Learn device for measuring properties and method.
Background technology
Soft material is the material that the class between solid and perfect fluid is special, is usually by dividing greatly Son or molecular cluster composition, it has flexibility and two distinguishing features of complexity.Soft material mainly wraps Including rubber, biological tissue and liquid crystal, it contacts closely with our daily life, with general Engineering material is compared, and soft material has unique good characteristic, as rubber have corrosion-resistant, The advantages such as pliable and tough, wear-resisting, adiabatic insulation, in Aero-Space, biomaterial, Industrial Engineering and medical science In field, there is extensive application background.Therefore, the test to soft material is extremely important, knows soft material Performance after, just can sit in the right seat and make its performance using value that puts into production.
The mechanical property of soft material is complex, and small effect the most to external world is very sensitive, to soft Material applies relatively side crops industry just can produce moderate finite deformation, and the most weak impact causes strong change, and soft material Deformation response there is nonlinear feature, including geometrical non-linearity and physical nonlinearity, it addition, soft Material Contact Boundary in contact problems is also nonlinear, so the test of soft material mechanical property Extremely complex.
In prior art, the Mechanics Performance Testing for soft material has had some research approaches, such as CN 201210319723.9 Multipurpose in-situ micro-scale mechanics performance test methods under disclosed ESEM, It uses voice coil motor to avoid the produced vibration of driving stepper motor mode, can carry out original position stretching, Compression, bending and fatigue mechanics performance test.But the data that the method obtains power need an additional power Sensor, and fatigue crack situation need to be obtained by ESEM, it is simultaneous for the sample of different length Need to design slide block and chute, structure is complicated, operation inconvenience.
Summary of the invention
For disadvantages described above or the Improvement requirement of prior art, the invention provides a kind of soft material mechanics Device for measuring properties and method, it realizes loading the collection with data by voice coil motor, and utilizes Computer sends the motion of order-driven voice coil motor, contacts laboratory sample by the main shaft of voice coil motor, Sample is applied certain load, obtains displacement and load data, and combine digital picture to soft material Make to measure further, obtain material more fully mechanical property parameters, there is certainty of measurement high, measure The advantages such as scope is wide, it is adaptable to the measurement of the multiple mechanical property of multiple soft material.
For achieving the above object, according to one aspect of the present invention, the present invention proposes a kind of soft material Mechanical property measuring device, it is characterised in that this measurement apparatus includes voice coil motor, controller, meter Calculation machine, translation stage and ccd video camera, wherein:
Described voice coil motor is installed on stand, and it is by controller control, and it includes being located at its internal grid Chi, force snesor and main shaft, described controller is connected with computer, its finger sent according to computer Order drives voice coil motor vertically to move along a straight line, and master grating scale and force snesor obtained The displacement of axle and load data send to computer, to obtain the load-displacement relation of soft material to be measured: S=f (F), wherein, S is the main shaft displacement relative to workpiece origin, and F is the power of main shaft feedback;
Described translation stage is located at the lower section of voice coil motor, it is used for place soft material to be measured, to be measured The side of soft material is provided with ccd video camera, before this ccd video camera is used for shooting soft material pressurization After deformation pattern, and by deformation pattern transmission in computer, it is thus achieved that the deformation data of soft material.
As it is further preferred that described workpiece origin determines in the following way: make voice coil motor Main shaft at full speed, the mode of low strength close to the surface of soft material to be measured, the most persistently monitor position Error, until site error arrives setting value, makes the position of main shaft keep constant, with this point for programming Initial point.
As it is further preferred that the speed of described high speed is specially 8000 μm/s, low strength is concrete For the gentle contact power less than 10 g.
As it is further preferred that described setting value is 50 μm.
As it is further preferred that described controller is connected with power transfer module, this Power convert mould Block and computer are directly by 220V Alternating Current Power Supply.
As it is further preferred that described stand includes base and the vertical plate being vertically mounted on base; Described controller and power transfer module are installed on the side of vertical plate;Described voice coil motor and translation stage It is installed on the opposite side of vertical plate.
As it is further preferred that be provided with reinforcement between described base and vertical plate.
It is another aspect of this invention to provide that provide a kind of soft material mechanical property measuring method, its profit Measure with described device, comprising:
Computer transmission program instructs to controller, and the main shaft of voice coil motor is edge under the driving of controller Vertical direction to move along a straight line, it is weak that voice coil motor realizes with soft material to be measured in the way of soft landing Power contacts;When the surface of main shaft with soft material to be measured just contacts, it is set to workpiece origin, afterwards Main shaft continues motion, and soft material produces deformation under the load effect of main shaft;Light within voice coil motor Main shaft displacement and load data that grid chi and force snesor obtain send to computer, soft material one to be measured The ccd video camera of side takes the photograph the deformation pattern before and after soft material pressurization, and by deformation pattern transmission to calculating To obtain deformation data in machine;By displacement and load data the deformation data combining deformation pattern, Quantitative scoring calculates the mechanical property parameters of soft material.
As it is further preferred that the mechanical property parameters of described soft material includes elastic modelling quantity, delayed Ring performance parameter and fatigue behaviour parameter.
As it is further preferred that described elastic modelling quantity computing formula is as follows:
E = PL 0 Δ L Δ A ;
Wherein, P is imposed load, L0For the overall length of soft material, Δ L is the deflection of soft material, and Δ A is Cross-sectional area during soft material measurement.
In general, by the contemplated above technical scheme of the present invention compared with prior art, mainly Possess following technological merit:
1. the main shaft of the voice coil motor of the present invention does straight line fortune along vertical direction under the driving of controller Dynamic, utilize soft landing functional realiey to contact with the low force of soft material sample, the most continuable monitoring position The error put, can arrange programming zero easily.
2. the actuator of the present invention can carry out the control of position, strength, speed and acceleration accurately, It is directly driven by controller, has the highest accuracy and repeatability, may be implemented in power, speed And freely change between the Three models of position.
3. the present invention measures the deformation data of soft material under small strain, and and sound by ccd video camera The load-displacement data of circle motor feedback combine, and can obtain material more fully mechanics fast and accurately Performance parameter.The many kinds of forces such as soft material elastic modelling quantity, mechanical property hysteresis loop, fatigue behaviour can be realized Learn the measurement of performance.
The compact overall structure of measurement apparatus the most of the present invention, multiple functional, certainty of measurement is high, measures model Enclose wide, it is adaptable to the measurement of the multiple mechanical property of multiple soft material.
Accompanying drawing explanation
Fig. 1 is the integral layout figure of the soft material mechanical property measuring device of the embodiment of the present invention;
Fig. 2 (a) and (b) are the stereograms of the soft material mechanical property measuring device of the embodiment of the present invention.
Detailed description of the invention
In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with accompanying drawing And embodiment, the present invention is further elaborated.Should be appreciated that described herein specifically Embodiment only in order to explain the present invention, is not intended to limit the present invention.Additionally, it is disclosed below Just may be used as long as technical characteristic involved in each embodiment of the present invention does not constitutes conflict each other To be mutually combined.
As it is shown in figure 1, a kind of soft material mechanical property measuring device that the embodiment of the present invention provides, its Mainly include voice coil motor 1, controller 2, computer 6, translation stage 4 and ccd video camera 8, this Invention mainly utilizes voice coil motor as actuator, and the force snesor directly using voice coil motor built-in is anti- Feedback force data, built-in grid chi feedback displacement data, thus Real-time Feedback while actuator motions Displacement-load data during soft material tension and compression deformation, by the soft landing function setting of voice coil motor Workpiece origin is to adapt to the soft material of differing heights.Concrete, measurement apparatus overall dimensions is 243mm ×260mm×360mm。
Separately below all parts in measurement apparatus is described in detail.
Voice coil motor 1, it is as the actuator of this measurement apparatus, is installed on stand 5, and it includes setting The grating scale in portion, force snesor and main shaft in the inner, this grating scale is for feeding back voice coil loudspeaker voice coil electric machine main shaft Position, i.e. provides positional information, and this force snesor is used for feeding back in loading procedure loading axle (i.e. main shaft) The data of power, i.e. provide force data, and this main shaft is for loading soft material.
Voice coil motor 1 is controlled by controller 2, and this controller 2 enters for the main shaft controlling voice coil motor Row linear motion, and by changing the size of main shaft displacement to change the load being applied to above soft material. Concrete, actuator voice coil motor 1 can be changed between power, speed and position Three models, I.e. sending force mode instruction to controller 2, the power with a certain size is travelled forward by actuator main shaft; To controller 2 transmission speed mode instruction, the speed with a certain size is travelled forward by actuator main shaft; Sending mode position instruction to controller 2, actuator main shaft will be moved to relative position or absolute position.
Controller 2 one end connects actuator (voice coil motor), and the other end is connected with computer (PC), The control instruction of sequencing is sent on controller 2 by PC end, to control the motion of voice coil motor.? When soft material is measured, obtain master respectively according to the grid chi within voice coil motor 1 and force snesor The displacement of axle and load data, this displacement and load data are directly gathered by controller, and pass through control The data gathered are sent to computer by device processed, and computer is analyzed according to the data gathered and locates Reason, to obtain load-displacement relation f of soft material to be measured:
S=f (F);
Wherein, S is the main shaft displacement relative to workpiece origin, and F is the power of main shaft feedback.
Further, workpiece origin (i.e. programming zero) determines in the following way: make voice coil motor 1 Main shaft at full speed, the mode of low strength close to the surface of soft material 7 to be measured, the most persistently monitor The following error of site error, i.e. main shaft, following error is requirement position and the actual bit of motion of main shaft The difference put, until following error reaches set site error, such as 50 μm, then makes main shaft Position keep constant, set this point as workpiece origin, perform the function after soft landing.Wherein, At high speed, to refer specifically to speed be 8000 μm/s to low strength, and strength is the gentle contact power less than 10 g.
More specifically, controller 2 is connected with power transfer module 3, this power transfer module 3 He Computer 6 is powered by same power supply 9, is specially directly by 220V Alternating Current Power Supply, controller 2 and electricity Source modular converter 3 is installed on the same side of stand 5.Controller 2 and the installation of power transfer module 3 Only need to play fixation, it is not necessary to machining accuracy and cooperation requirement, only need its installation site of reasonable layout Ensure compactedness and the integrality of outward appearance of structure.
Stand 5 is fixed for the installation realizing miscellaneous part, and for ensureing the stability measured, its Including base 51 and the vertical plate 52 being vertically mounted on base 51, controller 2 and Power convert mould Block 3 is located at the side of vertical plate 52, voice coil motor 1 and translation stage 4 and is located at another of vertical plate 52 Side.For the ease of measurement apparatus placement, take and measure time stability, need to ensure base 51 with Experimental bench has bigger contact area, and contact area needs finishing, and the bottom surface of base 51 selects The groove opening a wide 143mm can reduce finishing area.
Owing to voice coil motor moves along major axes orientation, therefore it is arranged on the vertical plate of stand, Main shaft is arranged along vertical direction, is arranged on vertical plate by such as fillister head screw, due to voice coil loudspeaker voice coil Motor 1 is arranged on vertical plate, and voice coil motor 1 is the main of soft material Mechanics Performance Testing device Parts, its installation accuracy directly affects the experimental precision of whole device, therefore, in the peace of vertical plate Finish on dress face.
For the ease of fixed installation, the base of stand is provided with four counter sinks, by mounting foot spiral shell Bolt fixes the test device of the present invention, and bolt head bottom surface need to be assembled with counter sink surface, therefore countersunk head Hole surface is matching surface, needs finishing.In order to improve the stability of vertical plate, at base with perpendicular Connected by welding procedure between straight plate and have reinforcement 53.
Translation stage 4 is used for placing and move horizontally test soft material, and it is arranged on voice coil motor 1 time Face, is fixed on the base of test device stand 5 by mounting foot bolt, and its installation accuracy is direct Affecting the experimental precision of whole device, for ensureing the accuracy of test, installed surface to ensure certain adding Work precision.
The side of soft material to be measured is provided with ccd video camera 8, and this ccd video camera 8 is used for shooting soft Deformation pattern before and after material pressurization, and by deformation pattern transmission to computer 6.Concrete, profit The digital picture on testee surface before and after deforming with video camera shooting, i.e. with CCD as photoelectric sensing Deflection in device monitoring materials in tension and compression deformation process, the method is not only measured than conventional extensometer Method is more objective, moreover it is possible to measure soft material whole deformation process, digital picture before and after finally deforming in real time Carry out coupling and obtain the deformation data of measured object, the width-telescopic amount etc. of such as material.
Wherein, before and after utilizing deformation, digital picture carries out the base that coupling obtains the deformation data of measured object Present principles is to take the certain pixel size centered by certain unknown point in the reference picture of CCD shooting Rectangle is the sub-district of reference picture, is scanned for by certain searching method after deformation in image, and Carry out correlation computations according to selected coefficient correlation, it is thus achieved that coefficient correlation take extreme value by certain put centered by The sub-district of target image, so that it is determined that the displacement in the sub-district of reference picture.Such as can select measured material wheel Exterior feature border point the most clearly is unknown point, and the rectangle taking certain pixel size centered by this point is ginseng Examining image subsection, after hierarchical loading, mate deformation pattern, before and after deformation, image subsection is the most similar Time coefficient correlation take minimum of a value, this region is the sub-district of target image, thus available test specimen surface Profile each point deflection.
The control of the measurement apparatus of the present invention is broadly divided into two parts, is motion control and data respectively Collection analysis controls.Motion control is completed by the communication of controller with computer, in computer and control When carrying out data communication between device processed, can use multiple programming language, these orders are led to by serial ports News, directly drive voice coil motor motion or preserve in memory.Data collection and analysis controls main It is the load-displacement data obtained by gathering in soft material Mechanics Performance Testing experiment, experimental data is entered Row analytical calculation, draws the mechanical property parameters of soft material.
The whole measurement apparatus of the present invention is controlled by the upper computer software in computer 6, including sound The motion of circle motor 1 main shaft, the pattern of the stress deformation curve of generation and the collection of experimental data with after Process.Translation stage 4 is manually controllable, it is possible to be designed as motor control.
Present invention also offers a kind of soft material mechanical property measuring method, itself particularly as follows:
Computer 6 transmission program instructs to controller 2, and the main shaft of voice coil motor 1 drives controller 2 Moving along a straight line along vertical direction under Dong, voice coil motor realizes and softwood to be measured in the way of soft landing The low force contact of material 7;When the surface of main shaft with soft material 7 to be measured just contacts, it is set to programming After initial point, main shaft continues motion, and soft material produces deformation under the load effect of main shaft;Voice coil motor 1 Internal grid chi and force snesor gather displacement and the load data of main shaft respectively, and by displacement and load Data are transmitted to computer 6, and the ccd video camera 8 of soft material 7 side to be measured shoots soft material pressurization Deformation pattern front and back, and by deformation pattern transmission to computer 6, to obtain the deformation of soft material Data;By displacement and load data the deformation data combining deformation pattern, quantitative scoring calculates softwood The mechanical property parameters of material.
Below as a example by soft material elastic modelling quantity, mechanical property hysteresis loop and fatigue test, retouch further State the test process of the present invention.
1) elasticity modulus test
Elastic modelling quantity computing formula is as follows:
E = PL 0 Δ L Δ A ;
Wherein, P is imposed load, and Δ L is the deflection of soft material, and Δ A is during soft material is measured Cross-sectional area, L0Overall length for soft material.
In test process, the cross-sectional area of soft material is being constantly occurring change, by digital correlation side After method (i.e. ccd video camera 8) measurement deformation, the profile of material is in the hope of cross-sectional area Δ A.Pass through sound Circle electric machine built-in grating scale records the deflection Δ L of soft material, by the force snesor that voice coil motor is built-in The imposed load P of material can be obtained, be fed back in computer to draw soft material under different distortion Elastic modelling quantity performance.
2) mechanical property hysteresis loop test
The measurement apparatus of the present invention can carry out material mechanical performance hysteresis loop test, should by drawing stress Varied curve i.e. can get the mechanical property hysteresis loop of soft material.Material is under cyclic loading, and its stress should Becoming response to be very different with dull loading, overall strain width includes bullet strain amplitude and plastic strain width:
Δ ε=Δ εe+Δεp
Wherein, Δ ε is overall strain width, Δ εeFor playing strain amplitude, Δ εpFor plastic strain width.Complete Load-deformation curve corresponding to load cycle surrounds a loop line closed, and claims hysteresis loop or delayed Ring.Experimentation is obtained by the stress and strain value during monitoring soft material loading and unloading The hysteretic properties of soft material.
3) fatigue test
The measurement apparatus of the present invention can carry out the fatigue test of soft material, by computer to controller 2 Send control instruction, make actuator voice coil motor apply alternate load to soft material, obtain test material Intensity under alternate load, is fatigue strength.
R = σ m i n σ max ;
Wherein, R is stress ratio, σminFor minimum load, σmaxFor maximum load, by computer Software records R=-1 time material cycle-index when being damaged and imposed load size, draw out table Show the S-N curve of relation between applied stress level and standard specimen fatigue life, i.e. can get softwood The fatigue behaviour of material.
As it will be easily appreciated by one skilled in the art that and the foregoing is only presently preferred embodiments of the present invention, Not in order to limit the present invention, all made within the spirit and principles in the present invention any amendment, etc. With replacement and improvement etc., should be included within the scope of the present invention.

Claims (10)

1. a soft material mechanical property measuring device, it is characterised in that this measurement apparatus includes voice coil loudspeaker voice coil Motor (1), controller (2), computer (6), translation stage (4) and ccd video camera (8), Wherein:
Described voice coil motor (1) is installed on stand (5), and it is controlled by controller (2), and it includes It is located at its internal grid chi, force snesor and main shaft;Described controller (2) and computer (6) phase Even, its order-driven voice coil motor (1) sent according to computer (6) vertically does straight line Motion, and the displacement of main shaft grating scale and force snesor obtained and load data transmission are to computer (6), to obtain the load-displacement relation of soft material to be measured (7): S=f (F), wherein, S is main Axle is relative to the displacement of workpiece origin, and F is the power of main shaft feedback;
Described translation stage (4) is located at the lower section of voice coil motor (1), it is used for place softwood to be measured Material (7), is provided with ccd video camera (8) in the side of soft material to be measured (7), and this CCD images The machine (8) deformation pattern before and after shooting soft material pressurization, and deformation pattern is transmitted to computer (6) in, it is thus achieved that the deformation data of soft material.
2. soft material mechanical property measuring device as claimed in claim 1, it is characterised in that described volume Cheng Yuandian determines in the following way: make the main shaft of voice coil motor (1) at full speed, the side of low strength Formula, close to the surface of soft material to be measured (7), the most persistently monitors site error, until site error arrives Reach setting value, make the position of main shaft keep constant, with this point as workpiece origin.
3. soft material mechanical property measuring device as claimed in claim 2, it is characterised in that described Speed at high speed is specially 8000 μm/s, and low strength is specially the gentle contact power less than 10 g.
4. soft material mechanical property measuring device as claimed in claim 2, it is characterised in that described Setting value is 50 μm.
5. soft material mechanical property measuring device as claimed in claim 4, it is characterised in that described Controller (2) is connected with power transfer module (3), this power transfer module (3) and computer (6) Directly by 220V Alternating Current Power Supply.
6. soft material mechanical property measuring device as claimed in claim 5, it is characterised in that described Stand (5) includes base (51) and the vertical plate (52) being vertically mounted on base (51);Institute State controller (2) and power transfer module (3) and be installed on the side of vertical plate (52);Described sound Circle motor (1) and translation stage (4) are installed on the opposite side of vertical plate (52).
7. soft material mechanical property measuring device as claimed in claim 6, it is characterised in that described Reinforcement (53) it is provided with between base (51) and vertical plate (52).
8. a soft material mechanical property measuring method, it is characterised in that it utilizes such as claim 1-7 Described device measures, comprising:
Computer (6) transmission program instructs to controller (2), and the main shaft of voice coil motor (1) is in control Moving along a straight line along vertical direction under the driving of device processed (2), voice coil motor is real in the way of soft landing Now the low force with soft material to be measured (7) contacts;When main shaft and soft material to be measured (7) surface just During contact, being set to workpiece origin, main shaft continues motion afterwards, and soft material is in the load effect of main shaft Lower generation deformation;Grating scale that voice coil motor (1) is internal and the main shaft displacement that force snesor obtains and load Lotus data send to computer (6), ccd video camera (8) shooting of soft material to be measured (7) side Deformation pattern before and after soft material pressurization, and deformation pattern is transmitted to computer (6) to obtain change Graphic data;By displacement and load data the deformation data combining deformation pattern, quantitative scoring calculates soft The mechanical property parameters of material.
9. soft material mechanical property measuring method as claimed in claim 8, it is characterised in that described The mechanical property parameters of soft material includes elastic modelling quantity, hysteresis loop performance parameter and fatigue behaviour parameter.
10. soft material mechanical property measuring method as claimed in claim 9, it is characterised in that described Elastic modelling quantity computing formula is as follows:
E = PL 0 Δ L Δ A ;
Wherein, P is imposed load, L0For the overall length of soft material, Δ L is the deflection of soft material, and Δ A is Cross-sectional area during soft material measurement.
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