CN106198225A - A kind of multi-scenarios method loading experimental apparatus of piezoelectric semiconductor fracture failure - Google Patents

A kind of multi-scenarios method loading experimental apparatus of piezoelectric semiconductor fracture failure Download PDF

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Publication number
CN106198225A
CN106198225A CN201610816629.2A CN201610816629A CN106198225A CN 106198225 A CN106198225 A CN 106198225A CN 201610816629 A CN201610816629 A CN 201610816629A CN 106198225 A CN106198225 A CN 106198225A
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CN
China
Prior art keywords
support arm
cuboid box
piezoelectric semiconductor
pedestal
experimental apparatus
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CN201610816629.2A
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Chinese (zh)
Inventor
秦国帅
赵炎翡
徐广涛
赵明皞
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Henan Ganlian Intelligent Technology Co ltd
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Zhengzhou University
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Priority to CN201610816629.2A priority Critical patent/CN106198225A/en
Publication of CN106198225A publication Critical patent/CN106198225A/en
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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
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058Kind of property studied
    • G01N2203/006Crack, flaws, fracture or rupture
    • G01N2203/0067Fracture or rupture
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02Details not specific for a particular testing method
    • G01N2203/022Environment of the test

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  • 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)
  • General Physics & Mathematics (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)

Abstract

The invention discloses the multi-scenarios method loading experimental apparatus of a kind of piezoelectric semiconductor fracture failure, including base plate, base plate is fixed with pedestal, top horizontal at pedestal is provided with dovetail chute, left support arm and right support arm is slidably connected in dovetail chute, described left support arm and right support arm are symmetrical, are provided with graduation mark at the top of pedestal front surface along dovetail chute axis direction;Being equipped with support roller groove at the top of left support arm and right support arm, be placed with backing roll in supporting roller groove, described backing roll uses isolation material, places sample to be tested on backing roll;Base plate is fixed with the located lateral end for positioning sample to be tested and longitudinal register pawl, the most also includes that open-topped cuboid box, the bottom surface of described cuboid box are insulant, be optical glass before cuboid box;It is achieved thereby that the multi-scenarios method loading experimental apparatus of piezoelectric semiconductor's fracture failure when a kind of mechanical stress fields, current field, high voltage field and coupling thereof.

Description

A kind of multi-scenarios method loading experimental apparatus of piezoelectric semiconductor fracture failure
Technical field
The invention belongs to piezoelectric semiconductor's technical field, particularly to the multi-scenarios method of a kind of piezoelectric semiconductor fracture failure Loading experimental apparatus.
Background technology
Along with semi-conducting material and the fast development of piezoelectric technology, it has been found that a kind of have the half of piezoelectric properties concurrently Conductor material i.e. piezoelectric semiconductor, such as CdS, CdSe, ZnO, AlN, GaN etc..Piezoelectric semiconductor has piezoelectric and quasiconductor Material dual physical characteristic, also has the advantages such as high heat conductance, high electronics drift velocity saturated, high and big disruptive critical voltage, So becoming development high-frequency high-power, high temperature resistant, Flouride-resistani acid phesphatase semiconductor microelectronics and the ideal material of circuit, navigate in aviation My god, military affairs, satellite communication, automobile, the field such as oil exploitation obtained the highest attention, have a wide range of applications.
During the use of electronic device, semiconductor device failure accounts for more than half that electronic device lost efficacy, quasiconductor Component failure is it is usually because the local stress of material internal has exceeded their maximum rating, before current technology Piezoelectric semiconductor's device on edge, the problem equally existing bigger crash rate, so the Damage and Failure to piezoelectric semiconductor's material Study particularly important.Experimentation to piezoelectric semiconductor's material failure mechanism, can improve piezoelectric semiconductor's device products Designing quality, is favorably improved the reliability of electronic equipment, the development speed to quickening piezoelectric semiconductor device, improves piezoelectricity half The yield rate of conductor device and reliability are respectively provided with important meaning.China is the most also strengthening failure analysis and failure mechanism The research of aspect, and establish some specialized laboratories, improve basis and the condition carrying out reliability consideration.But current research It is to launch research based on failure analysis with the fermentation such as detection technique, reliability evaluation mostly, and for the basis of semiconductor device Levy material damage mechanism the fewest with mathematical model aspect research, the fracture under piezoelectric semiconductor's material multi-scenarios method environment is lost The experimental provision that effect research is not more relevant.
It is said that in general, piezoelectric semiconductor's material is fragile material, during manufacturing, polarizing and use, it is possible to create as Crackle, hole, the defect such as it is mingled with;In actual application, piezoelectric semiconductor's device generally requires and bears harsh environment bar Part, such as mechanical stress fields, stress field, voltage field and current field etc., the most electrically stress, chemical stress, radiation stress and His factor all can cause piezoelectric semiconductor's device to show the strongest non-linear and big strain, easily occur near defect power and The concentration of electricity load, can cause Defect expanding under certain condition, ultimately cause the fracture failure of piezoelectric semiconductor's device.
Particularly piezoelectric semiconductor, itself possesses piezoelectric properties, can produce piezoelectric charge in stress or vibration processes, Extension on crackle or defect produces extremely complex impact, and therefore each stress field of experimentation and coupling stress field are to piezoelectricity The fracture failure mechanism of semi-conducting material, and sum up the fracture failure mathematical model of piezoelectric semiconductor's material, piezoelectricity is partly led The design of body device has highly important scientific meaning and practical value.Piezoelectric semiconductor's material has coupled piezoelectric and has partly led Body material dual physical property, research piezoelectric semiconductor Materials Fracture inefficacy mechanics experiment problem, need at mechanical stress fields, electricity Carry out under flow field, high voltage field and coupled field loading environment thereof;Piezoelectric semiconductor possesses the physical property of wide bandgap semiconductor, gives Piezoelectric semiconductor provides extra-high pressure field loading technique and common piezoelectricity dielectric material to have the biggest difference, and requires experiment dress Put and possess high regulation, storage, registration accuracy, it is also contemplated that the insulating properties that system is overall, therefore, to experiment charger It is proposed the highest requirement with loading insulation environment;But there is presently no for this fracture failure of piezoelectric semiconductor's material Mechanism carries out standard and the device studied and test.
Summary of the invention
The present invention seeks to propose the fracture of a kind of piezoelectric semiconductor for solving above-mentioned problems of the prior art to lose The multi-scenarios method loading experimental apparatus of effect, research is under mechanical stress fields, current field, high voltage field and coupled field loading environment thereof The fracture damage of piezoelectric semiconductor's material and fracture toughness, accumulation piezoelectric semiconductor material is for the sensitivity of different physical field environment Degree, thus explore the above-mentioned physical field micromechanism of damage to piezoelectric semiconductor's material, this sets improving piezoelectric semiconductor's device Meter quality has highly important scientific basis and practical value.
The present invention solves that the problems referred to above are adopted the technical scheme that: many couplings of a kind of piezoelectric semiconductor fracture failure Close loading experimental apparatus, including base plate, base plate is fixed with pedestal, be provided with in the middle at pedestal top further groove, The top horizontal of pedestal is provided with dovetail chute, slidably connects left support arm and right support arm and on left support arm and the right side in dovetail chute Being equipped with the first clamping screw on support arm, described left support arm and right support arm are symmetrical, at the top of pedestal front surface along dovetail Chute axis direction is provided with graduation mark;Support roller groove, the axle of described support roller groove it is equipped with at the top of left support arm and right support arm Line is perpendicular to dovetail chute axis, is placed with backing roll in supporting roller groove, and described backing roll uses isolation material and backing roll Having intensity and the hardness of corresponding requirements, place sample to be tested on backing roll, described support roller well width is backing roll diameter 1.1~1.3 times, support roller groove depth more than backing roll radius and less than support roller diameter.
Further, described backing roll two ends are equipped with annular groove;Left support arm or right support arm are provided with slide opening, described cunning Axially bored line is parallel with dovetail chute axis, slidably connects draw runner in slide opening, is provided with for tightly on left support arm or right support arm Gu the second clamping screw of draw runner, draw runner is provided with the graduation mark for indicating sliding distance, integrally sets in the outer end of draw runner Located lateral end, the end face of described located lateral end is had to be burnishing surface and align with sample to be tested end face;The end after pedestal Being fixed with slide on plate, be provided with slideway in slide, described slideway axis is vertical with dovetail chute axis, the company of slip in slideway It is connected to the slide plate being vertically arranged, slide is provided with the 3rd clamping screw for fastening slide plate, for indicating sliding distance Graduation mark, is integrally formed with longitudinal register pawl on the top of slide plate, and the end face of described longitudinal register pawl is burnishing surface and with to be tested Align in sample side.
Further, the medial surface top that described left support arm is relative with right support arm is chamfering.
Further, also include sample pressure head, described sample pressure head be fixedly arranged at the front end with loaded roll, described loaded roll uses absolutely Edge material and loaded roll have intensity and the hardness of corresponding requirements.
Further, also include that open-topped cuboid box, the bottom surface of described cuboid box are that politef is solid Body insulant, is optical glass before cuboid box, and the other three side of cuboid box is lucite;Described Base plate is fixed on the inner bottom surface of cuboid box by hexagon socket head cap screw, fills dimethicone and flood in cuboid box No sample to be tested, be provided with incoming line, line outlet, oil-in and oil-out in cuboid box side.
Further, the inner bottom surface of cuboid box is provided with the tapped blind hole matched with interior six square bolts.
The present invention is had the beneficial effect that this experimental provision is by further groove, the graduation mark of pedestal front surface, a left side The setting of support arm and right support arm achieves the experiment required precision to piezoelectric semiconductor's sample to be tested strong point centering, meets Fracture toughness requirement of experiment at single mechanical stress field action lower piezoelectric quasiconductor;Further, backing roll, the adding of sample pressure head Carry roller all to have employed silicon nitride ceramics isolation material and both met and test the requirement to insulation and also reached the intensity of corresponding requirements And hardness;Meanwhile, cuboid box uses durable lucite, is easy to the optical glass of observation experiment phenomenon, polytetrafluoroethyl-ne The bottom surface composition one of alkene insulation, and splendid attire has colorless and odorless, transparency height, the diformazan of insulation feature in cuboid box Base silicone oil, it is provided that the insulation environment of a kind of applicable current field, high voltage field and coupled field effect thereof, solves at loading current Occur puncturing air or high pressure arc discharge and affecting the problem of experimental data when field, high voltage field and coupled field thereof, thus real Piezoelectric semiconductor's fracture failure when having showed a kind of effective mechanical stress fields, current field, high voltage field and coupling thereof Multi-scenarios method loading experimental apparatus.
Accompanying drawing explanation
Fig. 1 is the perspective view of the present invention;
Fig. 2 is the perspective view in Fig. 1 along arrow A direction;
Fig. 3 is the perspective view of cuboid box;
Fig. 4 is the perspective view of sample pressure head.
Detailed description of the invention
Below in conjunction with the accompanying drawings the present invention is further described.
As depicted in figs. 1 and 2, the multi-scenarios method loading experimental apparatus of a kind of piezoelectric semiconductor fracture failure, including base plate 2, it is fixed with pedestal 18 on a base plate 2, is provided with in the middle at pedestal 18 top further groove 16, utilizes and further groove 16 is protected Card pedestal 18 is the precision of middle position when experiment, and the top horizontal at pedestal 18 is provided with dovetail chute 3, in dovetail chute 3 Slidably connect left support arm 12 and right support arm 5 and on left support arm 12 and right support arm 5, be equipped with the first clamping screw 4, a described left side Support arm 12 and right support arm 5 are symmetrical, are provided with graduation mark 17 at the top of pedestal 18 front surface along the sliding 3 groove axis directions of dovetail; Be equipped with support roller groove at the top of left support arm 12 and right support arm 5, the axis of described support roller groove is perpendicular to dovetail chute 3 axle Line, is placed with backing roll 7 in supporting roller groove, and described backing roll 7 uses isolation material and backing roll 7 to have the strong of corresponding requirements Degree and hardness, such as silicon nitride ceramics material, place sample to be tested 9 on backing roll 7, and described support roller well width is backing roll 7 1.1~1.3 times of diameter, support roller groove depth more than backing roll 7 radius and less than supporting roller 7 diameter.
In order to position sample to be tested 9 further, described backing roll 7 two ends are equipped with annular groove 11;Prop up on a left side Arm 12 or right support arm 5 are provided with slide opening 6, and described slide opening 6 axis is parallel with dovetail chute 3 axis, slidably connects in slide opening 6 Draw runner 15, is provided with the second clamping screw 13 for fastening draw runner 15 on left support arm 12 or right support arm 5, is provided with on draw runner 15 For indicating the graduation mark of sliding distance, it is integrally formed with located lateral end 10, described located lateral end 10 in the outer end of draw runner 15 End face be burnishing surface and align with sample to be tested 9 end face;It is fixed with slide 21, at slide on base plate 2 after pedestal 18 Being provided with slideway 22 in 21, described slideway 22 axis is vertical with dovetail chute 3 axis, slidably connects and be vertically arranged in slideway 22 Slide plate 19, slide 21 is provided with the 3rd clamping screw 23 for fastening slide plate 19, for indicating the scale of sliding distance Line 20, is integrally formed with longitudinal register pawl 8 on the top of slide plate 19, and the end face of described longitudinal register pawl 8 is burnishing surface and with to be measured Align in sample 9 side.
In order to prevent receiving left support arm 12 or right support arm 5 top when stress is bent downwardly deformation in the middle of sample to be tested 9 Touch and affect experimental data, the medial surface top that described left support arm 12 is relative with right support arm 5 is chamfering 14, also allows for treating Landing during test specimens fracture.
As shown in Figure 3 and Figure 4, in order to meet sample to be tested 9 two ends when loading current field, high voltage field and coupled field thereof Occur puncturing air or high pressure arc discharge and affecting experimental data, also include sample pressure head 28 and open-topped cuboid box Son 26, described sample pressure head 28 be fixedly arranged at the front end with loaded roll 29, described loaded roll 29 uses isolation material and loaded roll 29 to have There are intensity and the hardness of corresponding requirements, such as silicon nitride ceramics material;The bottom surface 27 of described cuboid box 26 is politef Solid insulating material, polytetrafluoroethylene solids insulant processes so that tying mutually with lucite or optical glass through sodium Close, be optical glass before cuboid box 26, facilitate observation experiment phenomenon, the other three side of cuboid box 26 For lucite;Described base plate 2 is fixed on the inner bottom surface of cuboid box 26, at cuboid box by hexagon socket head cap screw 1 Filling dimethicone in 26 and flood sample to be tested, dimethicone has colorless and odorless, transparency feature high, insulation is Optimum selection;It is provided with incoming line, line outlet, oil-in 25 and oil-out 24 in cuboid box 26 side, at oil-in simultaneously 25 and oil-out 24 at be equipped with control switch.
For the leaking outside of dimethicone after preventing life-time service, the inner bottom surface 27 of cuboid box 26 is provided with interior The tapped blind hole that six square bolts 1 match.
This experimental provision in use, if single mechanical stress field action, is first placed on test by this experimental provision Immediately below the pressure head of machine, the pressure head moving down testing machine can be positioned at further groove 16, to ensure pedestal 18 middle position Precision, then equidistantly slide left support arm 12 and right support arm 5 according to graduation mark about 17, is individually placed to by two backing rolls 7 Runner groove is interior and uses the rubber band of weak elasticity to hook in annular groove 11 so that backing roll 7 is carried out preliminary pre-determined bit, it is ensured that just Beginning span accurate, according to the size of sample to be tested 9, horizontally slip draw runner 15 will be laterally according to the graduation mark above it Positioning end 10 is had good positioning, and screws the second clamping screw 13;Put sample to be tested 9 and ensure its end face and located lateral end 10 end face Alignment, then sliding skateboard 19 being had good positioning by longitudinal register pawl 8 according to graduation mark 20, screw the 3rd clamping screw 23, it is ensured that Align with longitudinal register pawl 8 end face in sample to be tested 9 side;Finally located lateral end 10 and longitudinal register pawl 8 are removed and i.e. completed The placement of sample to be tested 9 ensure that sample to be tested 9 and to further groove 16, the high accuracy centering of the pressure head of testing machine;Can treat Test specimens 9 carries out fracture toughness experiment.
This experimental provision in use, if current field, high voltage field and coupled field effect thereof, first by sample pressure head 28 It is arranged on testing machine and changes original pressure head, then base plate 2 is fixed in cuboid box 26 by interior six square bolts 1 On bottom surface 27, this experimental provision being then placed on the underface of sample pressure head 28, the placement centering of sample to be tested 9 positions with upper State the experimental procedure carried out under single mechanical stress field action equally to repeat no more, in cuboid box 26, finally contain diformazan Base silicone oil also floods sample to be tested 9 and reaches suitable liquid level, then sample to be tested 9 can be carried out fracture toughness experiment, Due to dimethicone have that colorless and odorless, transparency be high, the feature of insulation thus meet the insulation environment required for experiment, Even if sample to be tested 9 breaks rear high-voltage output line and falls and also will not pass on miscellaneous equipment by electric charge in cuboid box 26, protect Demonstrate,prove the safety of experiment.
In describing the invention, it is to be understood that term " longitudinally ", " laterally ", "front", "rear", "left", "right", The orientation of the instruction such as " level ", " top ", " end ", " interior ", " outward " or position relationship are to close based on orientation shown in the drawings or position System, is only to describe rather than instruction or infer the device of indication or element must have spy for ease of describing the present invention and simplifying Fixed orientation, for specific azimuth configuration and operation, thus it is not intended that the present invention to be protected the restriction of content.
If being used herein the word such as " first ", " second " to if limiting parts, those skilled in the art should This is known: " first ", the use of " second " are intended merely to facilitate the description present invention and simplify description, as the most additionally stated, Above-mentioned word does not has special implication.
Last it is noted that above example is only in order to illustrate technical scheme, it is not intended to limit;Although With reference to previous embodiment, the present invention is described in detail, it will be understood by those within the art that: it still may be used So that the technical scheme described in foregoing embodiments to be modified, or wherein portion of techniques feature is carried out equivalent, But these amendment or replace, do not make appropriate technical solution essence depart from various embodiments of the present invention technical scheme spirit and Scope.

Claims (6)

1. the multi-scenarios method loading experimental apparatus of piezoelectric semiconductor's fracture failure, it is characterised in that include base plate, at base plate On be fixed with pedestal, be provided with further groove in the middle at pedestal top, the top horizontal at pedestal is provided with dovetail chute, swallow Slidably connect left support arm and right support arm in tail chute and on left support arm and right support arm, be equipped with the first clamping screw, a described left side Support arm and right support arm are symmetrical, are provided with graduation mark at the top of pedestal front surface along dovetail chute axis direction;At left support arm Being equipped with support roller groove with the top of right support arm, the axis of described support roller groove is perpendicular to dovetail chute axis, is supporting roller groove Inside being placed with backing roll, described backing roll uses isolation material and backing roll to have intensity and the hardness of corresponding requirements, in supporting Placing sample to be tested on roller, described support roller well width is 1.1~1.3 times of backing roll diameter, supports roller groove depth more than propping up Runner radius and less than support roller diameter.
The multi-scenarios method loading experimental apparatus of piezoelectric semiconductor the most according to claim 1 fracture failure, it is characterised in that Described backing roll two ends are equipped with annular groove;Being provided with slide opening on left support arm or right support arm, described slide opening axis is sliding with dovetail Fluted shaft line is parallel, slidably connects draw runner in slide opening, is provided with the second lock for fastening draw runner on left support arm or right support arm Tight bolt, is provided with the graduation mark for indicating sliding distance on draw runner, is integrally formed with located lateral end, institute in the outer end of draw runner The end face stating located lateral end is burnishing surface and aligns with sample to be tested end face;It is fixed with slide on base plate after pedestal, Be provided with slideway in slide, described slideway axis is vertical with dovetail chute axis, slidably connects and be vertically arranged in slideway Slide plate, is provided with the 3rd clamping screw for fastening slide plate, for indicating the graduation mark of sliding distance, at slide plate on slide Top is integrally formed with longitudinal register pawl, and the end face of described longitudinal register pawl is burnishing surface and aligns with sample to be tested side.
The multi-scenarios method loading experimental apparatus of piezoelectric semiconductor the most according to claim 2 fracture failure, it is characterised in that The medial surface top that described left support arm is relative with right support arm is chamfering.
The multi-scenarios method loading experimental apparatus of piezoelectric semiconductor the most according to claim 3 fracture failure, it is characterised in that Also include sample pressure head, described sample pressure head be fixedly arranged at the front end with loaded roll, described loaded roll uses isolation material and loaded roll There is intensity and the hardness of corresponding requirements.
5. according to the multi-scenarios method loading experimental apparatus of the piezoelectric semiconductor's fracture failure described in any one of Claims 1-4, its It is characterised by, also includes that open-topped cuboid box, the bottom surface of described cuboid box are polytetrafluoroethylene solids insulation Material, is optical glass before cuboid box, and the other three side of cuboid box is lucite;Described base plate leads to Cross hexagon socket head cap screw to be fixed on the inner bottom surface of cuboid box, in cuboid box, fill dimethicone and flood to be measured Sample, is provided with incoming line, line outlet, oil-in and oil-out in cuboid box side.
The multi-scenarios method loading experimental apparatus of piezoelectric semiconductor the most according to claim 5 fracture failure, it is characterised in that The inner bottom surface of cuboid box is provided with the tapped blind hole matched with interior six square bolts.
CN201610816629.2A 2016-09-12 2016-09-12 A kind of multi-scenarios method loading experimental apparatus of piezoelectric semiconductor fracture failure Pending CN106198225A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107132130A (en) * 2017-06-14 2017-09-05 黄河科技学院 A kind of 3 points, four-point bending test machine adjusts fixture with centering
CN111122303A (en) * 2019-12-26 2020-05-08 西安交通大学 Size-adjustable pressurizing, fixing and centering device and centering method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN202362206U (en) * 2011-11-25 2012-08-01 苏州热工研究院有限公司 Three-point bending jig for precrack and fracture toughness test
CN102706726A (en) * 2012-04-24 2012-10-03 清华大学 Force-electricity coupling dynamic fracture experimental system
CN206074358U (en) * 2016-09-12 2017-04-05 郑州大学 A kind of multi- scenarios method loading experimental apparatus of piezoelectric semiconductor's fracture failure

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN202362206U (en) * 2011-11-25 2012-08-01 苏州热工研究院有限公司 Three-point bending jig for precrack and fracture toughness test
CN102706726A (en) * 2012-04-24 2012-10-03 清华大学 Force-electricity coupling dynamic fracture experimental system
CN206074358U (en) * 2016-09-12 2017-04-05 郑州大学 A kind of multi- scenarios method loading experimental apparatus of piezoelectric semiconductor's fracture failure

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107132130A (en) * 2017-06-14 2017-09-05 黄河科技学院 A kind of 3 points, four-point bending test machine adjusts fixture with centering
CN111122303A (en) * 2019-12-26 2020-05-08 西安交通大学 Size-adjustable pressurizing, fixing and centering device and centering method

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Application publication date: 20161207