CN106404535B - Test specimen component and test method for rock type III fracture toughness testing - Google Patents
Test specimen component and test method for rock type III fracture toughness testing Download PDFInfo
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- CN106404535B CN106404535B CN201610874392.3A CN201610874392A CN106404535B CN 106404535 B CN106404535 B CN 106404535B CN 201610874392 A CN201610874392 A CN 201610874392A CN 106404535 B CN106404535 B CN 106404535B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N1/00—Sampling; Preparing specimens for investigation
- G01N1/28—Preparing specimens for investigation including physical details of (bio-)chemical methods covered elsewhere, e.g. G01N33/50, C12Q
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Abstract
The invention discloses a kind of test specimen components and test method for rock type III fracture toughness testing, test specimen component includes test specimen ontology and pressure head with grooving, test specimen ontology is in disk form, grooving disposed thereon is the identical grooving of four shapes, it is located at test specimen ontology orthogonal two diametrically, four groovings extend through the upper and lower end face of test specimen ontology along the thickness direction of test specimen this body side surface to test specimen body central opening, to body interior；Pressure head is the identical arc end face pressure head of four shapes, it is same diametrically that two pressure heads are symmetrically positioned in one side end face of test specimen ontology, it is same diametrically that another two pressure head is symmetrically positioned in another side end face of test specimen ontology, and two diameters are mutually perpendicular to and respectively with two diameters where grooving in 45 ° of angles.Test specimen component level is placed on the workbench of universal testing machine when test, universal testing machine is used to carry out load to test specimen ontology by the pressure head of test specimen component until test specimen ontology fails in a manner of Bit andits control.
Description
Technical field
The invention belongs to rock mechanics and engineering fields, in particular to are used for the test specimen of rock type III fracture toughness testing
Component and test method.
Background technique
In rock engineering, in order to ensure the safety and stability of engineering structure, need that rock is avoided to be broken, and
In tunnel piercing, slope excavating, oil-gas mining, and needs to accelerate phenomenon of rupture, improves efficiency of breaking rock.Rock fracture toughness is made
To characterize the mechanics parameter that rock material resists fracture in rock fracture mechanics, weight is all had in engineer application and theoretical research
The value wanted.According to the difference of cracks in body load mode, fracture can be divided into I type (opening mode), II type (inplane shear
Type) and three kinds of basic models of type III (shear outside the plane type, also known as tearing mode), correspondingly, fracture toughness can also be subdivided into I type, II
Type and type III fracture toughness, i.e. KIc、KIIcAnd KIIIc.In the structure design, security evaluation and numerical simulation of rock engineering,
KIc、KIIcAnd KIIIcOften indispensable basic mechanical parameter.Therefore, easy test method is developed accurately to test
Fracture toughness is an important subject in rock fracture mechanics.
In recent years, many researchers have carried out a large amount of research, but the existing big spininess of research to rock fracture toughness test
Pair be I type or II type fracture toughness, it is relatively fewer for the research of type III fracture toughness testing, this is because: in laboratory
It is interior, I type and II type load are applied to test specimen and are easier, and to apply type III load generally require sufficiently complex device and
Very cumbersome operation.Therefore, it is necessary to which it is tough to develop type III fracture of the simple and feasible test method for testing rock material
Degree, for practical engineering application.
CN103471935A discloses a kind of for testing the test specimen of III type fracture toughness of plastic material, which is rectangular
Shape flat test piece, long side > broadside > thickness are symmetrical arranged two perpendicular to long side in the middle position of two long sides of plate
Symmetrical V-type side grooving, the examination is arranged in two surfaces of initial cut crackle, ligament that is remaining after grooving, playing connection function
Part can complete test on general universal testing machine.But if the test specimen is applied to III type fracture toughness of rock material
Test, will be present following deficiency: (1) rock material is usually to be obtained by way of drill core in building-site, obtained rock
In cylindrical body, the difficulty for processing rectangularity thin plate is larger；(2) test specimen needs to make shallower V-type grooving, this V-type grooving
Production gets up extremely to be not easy, and especially for coarse grained rock material, is easy to cause additional damage to test specimen, influences test specimen
Precision；It (3) when being tested using the test specimen is loaded by 4 angle points of the support base fulcrum to rectangle test specimen, application
Load is point loading, and loading position is exactly in rectangle test specimen angle point, this loading method implement it is very difficult, be easy because
Load angle point cracks prior to Near A Crack Tip and causes test failure；(4) how type III is calculated in the invention and after undeclared test
Fracture toughness, thus and it is incomplete.
Summary of the invention
Structure is complicated for existing type III fracture toughness testing test specimen, manufacture difficulty is big and the not no III of mature and feasible
The state of the art of type fracture toughness testing method, the present invention is intended to provide being used for the test specimen group of rock type III fracture toughness testing
It is disconnected to fill up rock type III in the prior art to simplify the structure of rock type III fracture toughness testing component for part and test method
Split the missing of toughness test method.
Provided by the present invention for the test specimen component of rock type III fracture toughness testing, including the test specimen ontology with grooving
With the pressure head for compressing test specimen ontology, the test specimen ontology is in disk form, and grooving disposed thereon is the identical grooving of four shapes,
It is located at ontology orthogonal two diametrically, four groovings are along the thickness direction of test specimen this body side surface into test specimen ontology
Heart line opening, the upper and lower end face that test specimen ontology is extended through to body interior；The pressure head is that four shapes are identical and test specimen
Transverse plane is at the arc end face pressure head of point contact, and it is same diametrically that two pressure heads are symmetrically positioned in one side end face of test specimen ontology, another two
It is same diametrically that pressure head is symmetrically positioned in another side end face of test specimen ontology, two diameters be mutually perpendicular to and respectively with two diameters where grooving
In 45 ° of angles, the vertical range of each pressure head and the contact point of test specimen ontology to this body side surface of test specimen is equal.
In the technical solution of above-mentioned test specimen component, the pressure head is viscous in its planar base surface mode parallel with test specimen ontology end face
It is attached on test specimen ontology end face.
In the technical solution of above-mentioned test specimen component, the ratio between radius of thickness of test specimen ontology and test specimen ontology for 0.2~
0.4。
In the technical solution of above-mentioned test specimen component, the ratio between the depth of grooving and the radius of test specimen ontology are 0.4~0.6.
In the technical solution of above-mentioned test specimen component, the radius of test specimen ontology is at least 25mm, and the width of grooving is no more than
1mm。
In the technical solution of above-mentioned test specimen component, the end of pressure head is spherical surface or ellipsoid pressure head；It is preferred that hemisphere pressure head
Or semiellipsoid pressure head.
In the technical solution of above-mentioned test specimen component, pressure head and the contact point of test specimen ontology to test specimen this body side surface it is vertical away from
From arriving the distance of test specimen body end horizontal edge, preferably 5~10mm.
The present invention also provides tested using above-mentioned test specimen component for rock type III fracture toughness testing component
Method: test specimen component level is placed on the workbench of universal testing machine, uses universal testing machine with the side of Bit andits control
Formula carries out load to test specimen ontology until test specimen ontology fails by the pressure head of test specimen component, and loading direction is perpendicular to test specimen ontology
Upper and lower end face, record test specimen ontology peak value fail load Pmax, rock type III fracture toughness K is calculated by formula (I)IIIc:
In formula (I), S be any pressure head and test specimen ontology contact point to the pressure head place test specimen ontology end face center of circle away from
From to the vertical range of this body side surface of test specimen, a is the depth of grooving, B and R difference for the contact point of S=R- pressure head and test specimen ontology
For the thickness and radius of test specimen ontology, Y is the geometric shape coefficient of test specimen, and Y value is calculated using finite element numerical software.
In the technical solution of above-mentioned rock type III fracture toughness testing method, use universal testing machine with Bit andits control
When mode loads test specimen by the pressure head of test specimen, control loading speed makes test specimen ontology fail at 30~60 seconds.Test specimen
Ontology failure refers to that test specimen ontology is destroyed and loses bearing capacity completely.
In the technical solution of above-mentioned rock type III fracture toughness testing method, the size of the geometric shape coefficient Y value of test specimen
It is related with the factors such as the setting position of the depth of grooving, the radius of test specimen ontology and pressure head, utilize finite element numerical software meter
The method for calculating Y value is as follows:
In the finite element numericals software for calculation such as engineering circles common ANSYS or ABAQUS, establish with test specimen ontology at appoint
The finite element numerical model of one ratio, the position corresponding with test specimen ontology load(ing) point in the finite element numerical model of test specimen ontology
Place applies Arbitrary Load P, then utilizes the type III stress strength factor K of finite element numerical software for calculation output crack tipIII,
Y value is calculated by formula (II):
In formula (II), B ', R ' and a ' are the geometric parameter of the finite element numerical model of test specimen ontology, in test specimen ontology
B, the physical significance of R and a is identical, and S ' is load(ing) point in the finite element numerical model of test specimen ontology to test specimen sheet where the load(ing) point
The distance in the body end face center of circle, it is identical as the physical significance of S in test specimen ontology, and be same between these corresponding geometric parameters
One ratio.
Compared with prior art, the invention has the following advantages:
1. the present invention provides a kind of new structural test specimen component for rock type III fracture toughness testing, the examination
Part component is made of the disc test specimen ontology with straight side grooving and pressure head, the cylinder that test specimen ontology can be drilled through by building-site
Shape core obtains after simply cutting, and it is the production for completing the test specimen that seaming chuck is then bonded on test specimen ontology, due to disk
Shape test specimen ontology can reduce cutting processing amount, and straight side grooving can effectively reduce difficulty of processing, especially for coarse grained rock
Stone material, moreover it is possible to reduce test specimen damage when processing, improve machining accuracy, with the existing rectangular flat plate with V-type side grooving
Test specimen is compared, and not only production method is simple, difficulty of processing is low for test specimen component of the present invention, and can improve the processing essence of test specimen
Degree.
2. the test specimen component of the present invention for rock type III fracture toughness testing is by pressure head on test specimen ontology
Ingenious arrangement cooperates general universal testing machine that can realize by pressure head and loads to the type III of crackle, in addition loading position with
The form of grooving and position setting rationally, will not cause to try when load because load(ing) point cracks prior to Near A Crack Tip on test specimen ontology
Failure is tested, compared with traditional type III fracture toughness testing test specimen, without with the use of complicated load and clamping device
Realize the load of type III load, moreover it is possible to avoid complicated load operation, test specimen of the present invention has loading method simply, easily
Operate and be conducive to improve the advantage of loading accuracy.
3. the present invention also provides the method for carrying out rock type III fracture toughness testing using above-mentioned test specimen component, the party
Method cooperates common universal testing machine that load, and the operation of this method can be realized using test specimen component provided by the invention
The equal very simple of calculating process of journey and rock type III fracture toughness, therefore this method is in test specimen production, device requirement, test
It is all had great advantages in process and input, this method has filled up rock type III fracture toughness testing in the prior art
Missing, can effectively solve the actual demand in rock engineering to simple and feasible type III fracture toughness testing method, practicability
By force, be conducive to promote and apply.
Detailed description of the invention
Fig. 1 is the perspective view of the test specimen component of the present invention for rock type III fracture toughness testing；
Fig. 2 is the top view of the test specimen component of the present invention for rock type III fracture toughness testing；
Fig. 3 is the load schematic diagram of the method for the invention；
In figure, any pressure head of 1-test specimen ontology, 2-groovings, 3-pressure heads, R-test specimen ontology radius, S-and test specimen
Distance of the contact point of ontology to the test specimen ontology end face center of circle where the pressure head, B-test specimen ontology thickness, a-grooving depth
Degree, t-grooving width, d-hemisphere pressure head diameter.
Specific embodiment
By the following examples and in conjunction with attached drawing to the test specimen group of the present invention for rock type III fracture toughness testing
Part and test method further illustrate.It is necessary to it is pointed out here that, the following examples are only intended to preferably illustrate of the invention
Working principle and its practical application, in order to which the present invention is used in the various facilities in its field by the technical staff in other fields,
And it is improved according to the imagination of various special-purposes.Although the present invention, which has passed through text, discloses its preferred embodiment, lead to
It crosses and reads these technology explanatory notes and can be appreciated that optimization property and alterability therein, and without departing from the scope of the present invention
It mentally improves, but such improvement should still fall within the protection scope of the claims in the present invention.
Embodiment 1
In the present embodiment, the structure of the test specimen component for rock type III fracture toughness testing is as shown in Fig. 1~2, the examination
Part ontology is cut through diamond slice machine-cut by the cylindrical core that construction site drills through and is made.
For the test specimen component of rock type III fracture toughness testing, by the test specimen ontology 1 with grooving 2 and test specimen sheet is compressed
The pressure head 3 of body forms, and the test specimen ontology 1 is in disk form, radius R=50mm, the thickness B=of the disc test specimen ontology
10mm, grooving 2 disposed thereon are the identical grooving of four shapes, are located at ontology orthogonal two diametrically, four
Grooving along the thickness direction of test specimen this body side surface to test specimen body central line opening, test specimen sheet is extended through to body interior
The upper and lower end face of body, the width t=1mm of the depth a=25mm of grooving, grooving；The pressure head 3 is that four diameter d are 10mm
Steel hemisphere, each pressure head is adhered on test specimen ontology end face in its planar base surface mode parallel with test specimen ontology end face, two
A pressure head is symmetrically positioned in that one side end face of test specimen ontology is same diametrically, and another two pressure head is symmetrically positioned in another side end face of test specimen ontology
It is same diametrically, two diameters be mutually perpendicular to and respectively with grooving where two diameters connect in 45 ° of angles, each pressure head with test specimen ontology
The vertical range of contact to this body side surface of test specimen is 5mm, i.e., test specimen where the contact point of pressure head and test specimen ontology to the pressure head
The distance S in the ontology end face center of circle is 45mm.
Embodiment 2
In the present embodiment, the structure of the test specimen component for rock type III fracture toughness testing is as shown in Fig. 1~2, the examination
Part ontology is cut through diamond slice machine-cut by the cylindrical core that construction site drills through and is made.
For the test specimen component of rock type III fracture toughness testing, by the test specimen ontology 1 with grooving 2 and test specimen sheet is compressed
The pressure head 3 of body forms, and the test specimen ontology 1 is in disk form, radius R=60mm, the thickness B=of the disc test specimen ontology
24mm, grooving 2 disposed thereon are the identical grooving of four shapes, are located at ontology orthogonal two diametrically, four
Grooving along the thickness direction of test specimen this body side surface to test specimen body central line opening, test specimen sheet is extended through to body interior
The upper and lower end face of body, the width t=1mm of the depth a=36mm of grooving, grooving；The pressure head 3 is that four diameter d are 10mm
Steel hemisphere, each pressure head is adhered on test specimen ontology end face in its planar base surface mode parallel with test specimen ontology end face, two
A pressure head is symmetrically positioned in that one side end face of test specimen ontology is same diametrically, and another two pressure head is symmetrically positioned in another side end face of test specimen ontology
It is same diametrically, two diameters be mutually perpendicular to and respectively with grooving where two diameters connect in 45 ° of angles, each pressure head with test specimen ontology
The vertical range of contact to this body side surface of test specimen is 10mm, i.e., test specimen where the contact point of pressure head and test specimen ontology to the pressure head
The distance S in the ontology end face center of circle is 50mm.
Embodiment 3
In the present embodiment, the structure of the test specimen component for rock type III fracture toughness testing is as shown in Fig. 1~2, the examination
Part ontology is cut through diamond slice machine-cut by the cylindrical core that construction site drills through and is made.
For the test specimen component of rock type III fracture toughness testing, by the test specimen ontology 1 with grooving 2 and test specimen sheet is compressed
The pressure head 3 of body forms, and the test specimen ontology 1 is in disk form, radius R=25mm, the thickness B=5mm of the disc test specimen ontology,
Grooving 2 disposed thereon is the identical grooving of four shapes, is located at ontology orthogonal two diametrically, four groovings are equal
Along test specimen this body side surface thickness direction to test specimen body central line opening, the upper of test specimen ontology is extended through to body interior
Lower end surface, the width t=0.8mm of the depth a=10mm of grooving, grooving；The pressure head 3 is the steel that four diameter d are 8mm
Hemisphere, each pressure head are adhered on test specimen ontology end face in its planar base surface mode parallel with test specimen ontology end face, two pressure heads
It is same diametrically to be symmetrically positioned in one side end face of test specimen ontology, it is same straight that another two pressure head is symmetrically positioned in another side end face of test specimen ontology
On diameter, two diameters are mutually perpendicular to and respectively with two diameters where grooving in 45 ° of angles, and the contact point of each pressure head and test specimen ontology is arrived
The vertical range of this body side surface of test specimen is 5mm, i.e., test specimen body end where the contact point of pressure head and test specimen ontology to the pressure head
The distance S in the face center of circle is 20mm.
Embodiment 4
In the present embodiment, the type III fracture using the cooperation universal testing machine test rock of test specimen component described in embodiment 1 is tough
Degree operates as follows:
Test specimen component level described in embodiment 1 is placed on the workbench of universal testing machine, the upper of test specimen ontology is made
End face upward, lower end it is face-down, use universal testing machine to add by the pressure head of test specimen to test specimen in a manner of Bit andits control
It carries until test specimen ontology fails, for loading direction perpendicular to the bottom surface of hemi-spherical indenter, controlling loading speed makes test specimen 30~60
Second failure, load schematic diagram load P as shown in figure 3, the peak value of record test specimen ontology failsmax, rock type III is calculated by formula (I)
Fracture toughness KIIIc,
In formula (I), S be any pressure head and test specimen ontology contact point to the pressure head place test specimen ontology end face center of circle away from
From to the vertical range of this body side surface of test specimen, a is the depth of grooving, B and R difference for the contact point of S=R- pressure head and test specimen ontology
For the thickness and radius of test specimen ontology, Y is the geometric shape coefficient of test specimen, and Y value is calculated using finite element numerical software.
The method for calculating Y value using finite element numerical software is as follows:
In the finite element numericals software for calculation such as engineering circles common ANSYS or ABAQUS, establish with test specimen ontology at appoint
The finite element numerical model of the test specimen ontology of one ratio, in the finite element numerical model of test specimen ontology with test specimen ontology load(ing) point
Apply Arbitrary Load P at corresponding position, then the type III stress using finite element numerical software for calculation output crack tip is strong
Spend factor KIII, Y value is calculated by formula (II),
In formula (II), B ', R ' and a ' are the geometric parameter of the finite element numerical model of test specimen ontology, in test specimen ontology
B, the physical significance of R and a is identical, and S ' is load(ing) point in the finite element numerical model of test specimen ontology to test specimen sheet where the load(ing) point
The distance in the body end face center of circle, it is identical as the physical significance of S in test specimen ontology, and be same between these corresponding geometric parameters
One ratio.
For the present embodiment, determining Y value is 1.113 according to the method described above.
By Y, Pmax, S, a, B and R value substitute into formula (I) in, rock type III fracture toughness K can be calculatedIIIc=
YPmaxS(πa)0.5/(BR2)=1.113Pmax×45×(25π)0.5/(10×502) (unit: MPam0.5), herein in calculating
PmaxWith newton (N) for unit.
Claims (10)
1. being used for the test specimen component of rock type III fracture toughness testing, it is characterised in that including the test specimen ontology with grooving (2)
(1) and the pressure head (3) of test specimen ontology is compressed, the test specimen ontology (1) is in disk form, and grooving (2) disposed thereon is four shapes
The identical grooving of shape is located at ontology orthogonal two diametrically, and four groovings are along the thickness side of this body side surface of test specimen
To the upper and lower end face for extending through test specimen ontology to test specimen body central line opening, to body interior；The pressure head (3) is four
A shape is identical and test specimen end face is at the arc end face pressure head of point contact, and it is same that two pressure heads are symmetrically positioned in one side end face of test specimen ontology
Diametrically, it is same diametrically to be symmetrically positioned in another side end face of test specimen ontology for another two pressure head, two diameters be mutually perpendicular to and respectively with
Two diameters where grooving are in 45 ° of angles, and the vertical range of each pressure head and the contact point of test specimen ontology to this body side surface of test specimen is equal.
2. being used for the test specimen component of rock type III fracture toughness testing according to claim 1, it is characterised in that the pressure head
It is adhered on test specimen ontology end face in its planar base surface mode parallel with test specimen ontology end face.
3. the test specimen component according to claim 1 or claim 2 for rock type III fracture toughness testing, it is characterised in that test specimen
The ratio between thickness (B) and the radius (R) of test specimen ontology of ontology are 0.2~0.4.
4. the test specimen component according to claim 1 or claim 2 for rock type III fracture toughness testing, it is characterised in that grooving
Depth (a) and the ratio between the radius (R) of test specimen ontology be 0.4~0.6.
5. the test specimen component according to claim 1 or claim 2 for rock type III fracture toughness testing, it is characterised in that test specimen
The radius (R) of ontology is at least 25mm, and the width (t) of grooving is no more than 1mm.
6. the test specimen component according to claim 1 or claim 2 for rock type III fracture toughness testing, it is characterised in that described
The end face of pressure head is spherical surface or ellipsoid.
7. being used for the test specimen component of rock type III fracture toughness testing according to claim 6, it is characterised in that the pressure head
For hemisphere pressure head or semiellipsoid pressure head.
8. the test specimen component according to claim 1 or claim 2 for rock type III fracture toughness testing, it is characterised in that pressure head
Vertical range with the contact point of test specimen ontology to test specimen this body side surface is 5~10mm.
9. the side tested using the test specimen component for being used for rock type III fracture toughness testing described in one of claim 1 to 8
Method, it is characterised in that: test specimen component level is placed on the workbench of universal testing machine, uses universal testing machine to be displaced
The mode of control by the pressure head of test specimen component carries out load to test specimen ontology until test specimen ontology fails, loading direction perpendicular to
The upper and lower end face of test specimen ontology, the peak value failure load P of record test specimen ontologymax, rock type III fracture toughness is calculated by formula (I)
KIIIc:
In formula (I), S is any pressure head at a distance from the test specimen ontology end face center of circle where the contact point of test specimen ontology to the pressure head, a
For the depth of grooving, B and R are respectively the thickness and radius of test specimen ontology, and Y is the geometric shape coefficient of test specimen, and Y value is using limited
First numerical software is calculated.
10. the method tested according to claim 9 for the test specimen component of rock type III fracture toughness testing,
When being characterized in that universal testing machine is used to load test specimen by the pressure head of test specimen in a manner of Bit andits control, control load
Rate makes test specimen ontology fail at 30~60 seconds.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN106932253B (en) * | 2017-04-17 | 2019-08-30 | 四川大学 | Test the test specimen component and test method of rock I-II mixed mode dynamic fracture toughness |
| CN109459306B (en) * | 2018-12-13 | 2022-03-08 | 芜湖富春染织股份有限公司 | Yarn annular strength detection device |
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|---|---|---|---|---|
| JPH07225180A (en) * | 1993-12-16 | 1995-08-22 | Kyocera Corp | Measuring method of fracture toughness |
| CN103471935A (en) * | 2013-09-06 | 2013-12-25 | 南京理工大学 | Test piece for fracture toughness of III type cracks |
| CN106546477A (en) * | 2016-10-08 | 2017-03-29 | 四川大学 | For the test specimen component and method of testing of the test of fragile material type III Dynamic Fracture Toughness |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6588283B2 (en) * | 2001-06-25 | 2003-07-08 | Ut-Battelle, Llc | Fracture toughness determination using spiral-grooved cylindrical specimen and pure torsional loading |
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|---|---|---|---|---|
| JPH07225180A (en) * | 1993-12-16 | 1995-08-22 | Kyocera Corp | Measuring method of fracture toughness |
| CN103471935A (en) * | 2013-09-06 | 2013-12-25 | 南京理工大学 | Test piece for fracture toughness of III type cracks |
| CN106546477A (en) * | 2016-10-08 | 2017-03-29 | 四川大学 | For the test specimen component and method of testing of the test of fragile material type III Dynamic Fracture Toughness |
Non-Patent Citations (2)
| Title |
|---|
| Determination of mode III fracture toughness for different materials using a new designed test configuration;M.R.M. Aliha，et al.;《Materials and Design》;20150812;863–871页 * |
| 边缘裂缝圆盘砂岩试体III 型断裂韧度量测之研究;郭俊志等;《岩土力学》;20160630;263-266页 * |
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