Development Of A New Experimental Technique For Dynamic .
Journal of Mining and Environment (JME)ShahroodUniversity ofTechnologyjournal homepage: www.jme.shahroodut.ac.irIranian Societyof MiningEngineering(IRSME)Vol. 11, No. 3, 2020, 909-920.DOI: 10.22044/jme.2020.9818.1903Development of a New Experimental Technique for Dynamic FractureToughness Measurement of Rocks using Drop Weight TestG. Khandouzi, H. Memarian and M.H. Khosravi*School of Mining Engineering, College of Engineering, University of Tehran, Tehran, IranReceived 20 June 2020; received in revised form 8 July 2020; accepted 9 July 2020KeywordsDynamic fracturetoughnessDrop weightNumerical simulationLimestoneAbstractThe dynamic fracture characteristics of rock specimens play an important role inanalyzing the fracture issues such as blasting, hydraulic fracturing, and design of supports.Several experimental methods have been developed for determining the dynamic fractureproperties of the rock samples. However, many used setups have been manufactured formetal specimens, and are not suitable and efficient for rocks. In this work, a new techniqueis developed to measure the dynamic fracture toughness of rock samples and fractureenergy by modifying the drop weight test machine. The idea of wave transmission barfrom the Hopkinson pressure bar test is applied to drop weight test. The intact samples oflimestone are tested using the modified machine, and the results obtained are analyzed.The results indicate that the dynamic fracture toughness and dynamic fracture energy havea direct linear relationship with the loading rate. The dynamic fracture toughness anddynamic fracture energy of limestone core specimens under the loading rates of 0.120.56kN/µS are measured between 9.6-18.51MPa m and 1249.73-4646.08J/m2,respectively. In order to verify the experimental results, a series of numerical simulationare conducted in the ABAQUS software. Comparison of the results show a goodagreement where the difference between the numerical and experimental outputs is lessthan 4%. It can be concluded that the new technique on modifying the drop weight testcan be applicable for measurement of the dynamic behavior of rock samples. However,more tests on different rock types are recommended for confirmation of the application ofthe developed technique for a wider range of rocks.1. IntroductionFracture mechanics has been applied for a varietyof rock engineering issues such as rock cutting,explosive fracturing, seismic events, and hydrofracturing, which is based on the Griffith theoryand the Irvin’s modification for cracked mediumunder the static or dynamic conditions [1].Understanding the behavior of the materials understatic or dynamic fracturing is essential. Thisbehavior is described by the fracture parameterssuch as the dynamic fracture energy and dynamicfracture toughness, indicating the resistance ofmaterials against the propagation of the preexisting cracks [2]. Earlier measurements of thestress intensity factor (SIF) followed the ASTMCorresponding author: mh.khosravi@ut.ac.ir (M.H. Khosravi).E399 standard method for static load. Due to thefact that most of the rocks are brittle with precracking fatigue properties, the above-mentionedASTM standard method is not so efficient [3].Therefore, the International Society for RockMechanics (ISRM) recommended three methodsfor determination of the static fracture parametersof core-based rock specimens [4]. ISRM suggestedthe Short Rod (SR) and the Chevron Bending (CB)tests for fracture test in 1988 [5] and the CrackedChevron Notched Brazilian Disc (CCNBD) in1995 [6]. In addition to the methods suggested byISRM for the static condition, many researchershave used different sample geometries to measure
Khandouzi et al./ Journal of Mining & Environment, Vol. 11, No. 3, 2020dynamic fracture parameters; for example, Chunanand Xiaohe (1990) used cubic-shaped samples of amarble specimen [7]. Wang et al. (2011-2009)have determined this property using the holedcracked flattened Brazilian discs and crackedstraight-through flattened Brazilian discs [8, 9].Nikita et al. (2009) have examined the static anddynamic SIF of a few different rock types [10].Chen et al. (2009) used NSCB and Dai et al. (20102011) tested CCNBD to determine the dynamicfracture toughness of granites [11, 12]. Recently,some researchers have used the notched semicircle bend specimens in order to specify the rockdynamic fracture features under different loadingrates [13, 14]. Liu et al. (2019) have investigate theeffects of two elliptical holes and four fissures onthe mechanical behavior of sandstone using theacoustic emission (AE) monitoring and digitalimage correlation (DIC) techniques [15]. Amongthe experimental methods proposed by ISRM andASTM for measurement of the dynamic fractureparameters, the Charpy impact test, the drop weighttest, and the Hopkinson pressure bar are the mostcommon experimental techniques illustrated inFigure 1, and the advantages and disadvantages ofthose techniques are summarized in Table 1.Alongside many published papers in the field ofrock fracture toughness estimation, the Hopkinsonpressure bar has been used to conduct the fracturetests in order to measure the dynamic stressintensity factor (DSIF). This test is useful formetallic materials and small piece of rockspecimens [20]. The Charpy test is used to measurethevalues [21]. The ASTM standard E208 hasbeen introduced the drop weight machine as astandard laboratory setup, which is able to test avariety of large specimens including the edgenotched specimens under the 3-point bending(3PB) mechanism. There are some limitations forusing the drop weight test. Those limitations aredue to a sudden impact in the drop weight test,which leads to a jump of the specimen from itssupports. It may result in a lack of recording of thereflected wave from the interface of the specimenand the tub head, therefore, the stress equilibriumduring the test may not be achieved. The rate andthe form of the compressive load depend on boththe specimen and the features of the machine.Moreover, great care should be taken ininterpreting experimental data due to the couplingeffects between the machine vibration and thewave propagation. In this situation, the loading ratecannot be well controlled; thus, multi-axialloadings are unreliable [22].Due to the limitations of the above-mentionedcommon experimental setups for measurement ofdynamic fracture toughness of rock samples, it hasbeen decided to develop a new experimentaltechnique for measurement of the rock dynamicfracture based on the drop weight test. In this paper,the rock dynamic fracture is studiedexperimentally. In the first step, the modified setupis introduced, and then the way of determinationdynamic fracture toughness is described. Finally,the test results of core specimens with the straightnotch crack in 3PB for the limestone are presentedand the comparison with the numerical results isdiscussed.a) Charpy Impact Test [16]b) Drop Weight Test [7]c) Hopkinson Pressure Bar [17]Figure 1. Most common experimental dynamic fracture tests.910
Khandouzi et al./ Journal of Mining & Environment, Vol. 11, No. 3, 2020Table 1. Advantages and disadvantages of most common experimental dynamic fracture tests [18, 19].NameAdvantagesCharpyImpact Test- Simple setupDrop WeightTest- Simple setup- Using a large specimen for testingHopkinsonPressure Bar- Inertia can be ignored- Specimen reaches stress equilibriumbefore failure-Loading sample with constant ratebefore failure pointDisadvantages-Specimen jumped off the supports-Extreme fluctuations in the recorded force-A lack of understanding of the inertia force due to stresswave propagation in Charpy specimen- Specimen jumped off the supports- Not satisfaction of the stress equilibrium- Not justifying inertia force-Using a small piece of rock specimenfalling weight on the transmission bar. Anotheradvantage of the modified setup system is that thelarger rock specimens could be tested in a varietyof forms including disc-shaped, cylindrical, andcubic.In order to measure the dynamic load applying tothe specimen, a strain gauge was mounted at theend of the transmission bar (Figure 2). The positionof the strain gauge on the transmission bar isextremely important as we have to deal with twoproblems. First, at high rates of loading, the strikermaterial’s inertia forces are not entirely negligiblein comparison to the contact forces between thespecimen and the striker. Another problem is thatthe measured strain is dependent on the distributionof load over the specimen/striker contact region[23].2. Modified drop weight testIn order to solve the above-mentioned limitationsof the common tests, the idea of wave transmissionbar was borrowed from the Hopkinson pressure bartest and applied to the drop weight test and amodified drop weight test setup was developed.The modified drop weight test apparatus isillustrated in Figure 2.By this technique, in the modified drop weight testsetup, the specimen won’t jump of when the weightis dropped. Consequently, it will easily achievestress equilibrium, and the reflected wave frominterface of specimen and tub head can berecorded. Furthermore, the rate and form of thecompressive loading is not dependent on thefeatures of the specimen and machine. As well, theaverage energy and the loading rate can be wellcontrolled by means of the height and weight ofFigure 2. A modified drop weight test setup for measurement of dynamic fracture toughness of rocksamples.911
Khandouzi et al./ Journal of Mining & Environment, Vol. 11, No. 3, 2020When the strain gauges are moved closer to thecontact surface, the inertia effects become smallerdue to the reduced intervening mass. By contrast,the contact force distribution effects can be reducedby moving the strain gauge away from the contactsurface. Therefore, strain gauge should be mountedon the correct position of the transmission bar toreduce errors due to inertia forces as well asdecrease force distribution. Also when wavepropagates along the transmission bar, the wavecontinually changes its amplitude and shape due todamping losses and wave dispersion [24]. As aresult, it is better to mount the strain gauge near thetub head to solve all the problems mentionedabove. Thus by analyzing a considerable number ofthe test results, it was concluded that in themodified drop weight test apparatus, the straingauge should be mounted on the transmission barin a 10 cm distance from the tub head (Figure 2).experiment’s analysis [24]. In addition, to save datadetected by strain gauge, a data acquisition systemshown in Figure 3 is used in this work. Thisconsists of a digital oscilloscope DS 1064 B thathas four-channel with 2Gsa/s sampling precision,and an electrical circuit includes an amplifier andWheatstone bridge and battery (6 volt).2.1. Strain gauge and recording systemSince dynamic tests are rather expensive and timeconsuming, the sensors and data logger must beable to record data at an appropriate speed [24]. Itthis type of test, strain gauges are often preferred.Dynamic strain measurement can be carried out bymeans of three different types of strain gauges, FoilStrain Gauge (FSG), Semiconductor Strain Gauge(SSG) and Polyvinylidene Fluoride strain gauge(PVDF). FSG is the most common sensor in theFigure 3. Data acquisition system used in this work.Input: .bmp imageEnter pixelvalueDynamic wave, detected by oscilloscope, isrecorded in the .rcd format, which can be processedand converted to bit map (.bmp) image files by theUltra-scope software. For digitizing the .bmpformat of images in Ultra-scope, an algorithm waswritten in the Matlab software, as illustrated in theflowchart of Figure 4.AnalyzeUse color filterfor pixelsOutput: data with.xlsx formatDesigned digit appliedon filter pixelsQuantity valueare obtainedFigure 4. A flowchart of the algorithm written in MATLAB.direct and indirect. Direct calibration has beenadopted to calibrate and convert voltage of outputof oscilloscope to the equivalent force. Calibrationand force–voltage graph for the Modified DropWeight machine is shown in Figure 5.2.2. Calibration of data acquisition systemSince the oscilloscope detects voltage, calibrationis necessary to find out an appropriate relationshipbetween the impact force and the reported voltage.There are basically two methods of calibration:912
Khandouzi et al./ Journal of Mining & Environment, Vol. 11, No. 3, 2020The primary output of oscilloscope contains noise,spectroscopic (peak) data, and sharp. Almost all thedetected signals are noise-contaminated, which isan unpleasant phenomenon. Hence, the noisereduction techniques are very essential toreproduce a more representative signal. In filteringa signal, if the applied filter is not appropriate, thefiltered signal might be deformed and some partsof data might be deleted. Amongst different filters,the Sovitzky-Golay (S-G) filter [25] was selectedbecause this filter reduced noise and kept thestructure of the original signal. For achieving amodel of output, a curve-fitting tool and S-G filterwas used in the Matlab software. The flowchart ofthe data acquisition system used for the modifieddrop weight test apparatus is illustrated in Figure 6.Figure 5. Calibration force–voltage relation graph.Figure 6. A flowchart of the data acquisition system.913
Khandouzi et al./ Journal of Mining & Environment, Vol. 11, No. 3, 2020A total number of 9 core specimens with a diameterof D 54 mm and a length of L 220 mm (L) wereprepared by means of a coring machine. A 1 mmthick initial crack with a height of a 20 mm wasmade in the middle of the length of the specimens,as illustrated in Figure 7.3. Material properties and specimenpreparationThe behavior of material, texture and mineralogicalpurity of specimen is important in the fracture tests.The specimen should have a linear elastic behavior,a uniform texture, and a high mineralogical purity.The macroscopic and microscopic studies on thelimestone specimens showed that the specimenswere compact with a uniform texture. They had ahigh mineralogical purity, and entirely consisted offinegrainbioclasticlimestonewithmicrocrystalline background texture. Therefore,the limestone was selected as an appropriate rockfor this work.For determination of the mechanical properties ofthe understudied limestone, the uniaxialcompressive strength (UCS) tests and the Braziliantensile strength tests were conducted. Rigid servocontrol press 450 tones capacity (MTS) was usedfor conducting the uniaxial compressive tests.During the test, strain gages were used to measurethe axial and lateral deformations of the sample.The properties of the understudied limestone arelisted in Table 2.Figure 7. Geometric detail of the core specimen.4. Experimental resultsAfter preparation of the specimen, a weight of 3 kgwas dropped from a height inside the drop weighttower. The impact of the drop weight wastransferred to the specimen through thetransmission bar (Figure 1). By adjusting the heightof the drop weight, different dynamic loading rateswere applied to the core specimens. The load wastransferred to the specimen, resulting in its fracture,and was calculated from the deformation recordedby the strain gauge. The images of some specimensafter failure and the load data recorded for Test 1 isshown in Figure 8.Table 2. Properties of limestone used in this work.E()()( )(GPa)73.50.057270026.59.85a) Some specimens after testingb) The load data recorded in Test 1Figure 8. Load data recorded and cores specimen with straight notched after test.A curve with the best fit for the data shown inFigure 8(b) has the following sinusoidal equation.( ) .( . ) .( . where t is the time and a1, a2, b1, b2, c1, c2 areconstant coefficients that differ for every test. Theconstant coefficients obtained for Test 1 are listedin Table 3.)(1) 0.9831914
Khandouzi et al./ Journal of Mining & Environment, Vol. 11, No. 3, 2020Table 3. Values of constant coefficients for the best sinusoidal curve fit obtained for Test he dynamic loading, supplied by Hopkinsonpressure bar, drop weight test has used a far-fieldpeak load to calculate the fracture toughness that islocally at the crack tip. In the modified drop weighttest, the dynamic fracture toughness can becalculated using the following equation [26]:( ) 0.25 ( / ) ( ( )/ʹ 2 ( ) [450.8531 ([3.33 ( ) ] .) ʹwhere S is the support span (m), a is the cracklength (m), D is the diameter of the core (m), P isthe applied load (N), and ʹ is the dimensionlessstress intensity factor.Having the dynamic fracture toughness and theelastic modulus (E), the fracture energy (G) can becalculated using the following equation [27].(2)) ( ) . ] .()(4)(3)The dynamic experimental results are listed inTable 4.Table 4. Results of experimental tests.Test No.Height of fallingweight (m)Loading rate(kN/µS)Maximum 226.53218.625.531The measured dynamic fracture toughness anddynamic fracture energy at different loading ratesare plotted in Figure 9. The results obtainedindicate that the dynamic fracture toughness of thelimestone core specimen for loading rates from0.12 to 0.56kN/µS was between 9.6 and18.51MPa. , which is linearly growing with increasein the loading rate. The range of dynamic fractureenergy is from 1249.73 to 4646.08 , in a linearform when the loading rate increases.Dynamic fracturetoughness( re energy( 0.254359.48a crack was introduced to the model, as illustratedin Figure 10.5. Numerical simulationsThe numerical simulations corresponding to theexperimental tests were done by means of theABAQUS software. For this purpose, a model ofthe core specimen was defined in the software andFigure 9. Dynamic fracture toughness and dynamicfracture energy versus loading rate.915
Khandouzi et al./ Journal of Mining & Environment, Vol. 11, No. 3, 2020Figure 10. 3D numerical model of core specimenTo calculate the dynamic fracture parameters by Jintegral, the far field stress caused dynamic forcethat has been measured during the experiment isnecessary to be linked to the near filed stressaround the crack tip. In addition, each element hasa feature providing flexibility for modelling ofdifferent geometry and structure including numberof nodes, degree of freedom, and so on. Anelement’s number of nodes determines how thenodal degrees of freedom will be interpolated overthe domain of the element. Near the crack tip, themesh should be fine, provide an accurate result,and be geometrically versatile. Thus 6-node lineartriangular prisms (C3D6) were used with a regulararrangement in the position of crack tip to simulatethe crack. According to the concept of J-integral, itis necessary to define several independent paths forestimation of the fracture parameters to avoidHourglass and locking in simulation. Therefore, an8-node linear brick with redefined sweep path(C3D8R) was used to create a circular path aroundthe crack tip to calculate the J-integral.Furthermore, to adapt the rest of the numericalmodel with the used element and reduce thecomputation time, an 8-node linear brick withoutredefine sweep path (C3D8) was used to completethe model.The J-integral method in the ABAQUS softwarewas verified by exact analytical solution of fracturemechanics and proved to be authentic forcomparison. In the J-integral method, a number ofindependence contour integrals are defined aroundthe tip according to the theorem of energyconservation. The form of these integrals can bewritten as follows: ( ᴦ)(5)(6)where w is the density of the strain energy, Γ is aclosed counter-clockwise contour presented inFigure 11, t is the traction vector defined by theoutward drawn normal n and t (t σn), σ is thestress tensor,is the strain tensor, u is thedisplacement vector, and dΓ is the ele
In order to verify the experimental results, a series of numerical simulation are conducted in the ABAQUS software. Comparison of the results show a good agreement where the difference between the numerical and experimental outputs is less . parameters, the Charpy impact test, the drop weight test, and the Hopkinson pressure bar are the most
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