Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping flaws under uniaxial compression

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1 Acta Mech. Sin. (2017) 33(2): DOI /s RESEARCH PAPER Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping flaws under uniaxial compression Lekan Olatayo Afolagboye 1,2 Jianming He 1 Sijing Wang 1 Received: 14 July 2016 / Revised: 28 September 2016 / Accepted: 1 November 2016 / Published online: 27 December 2016 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016 Abstract Failure of rock mass that is subjected to compressive loads occurs from initiation, propagation, and linkage of new cracks from preexisting fissures. Our research investigates the cracking behaviour and coalescence process in a brittle material with two non-parallel overlapping flaws using a high-speed camera. The coalescence tensile crack and tensile wing cracks were the first cracks to occur from the preexisting flaws. The initiation stresses of the primary cracks at the two tips of each flaw were simultaneous and decreased with reduced flaw inclination angle. The following types of coalescence cracks were identified between the flaws: primary tensile coalescence crack, tensile crack linkage, shear crack linkage, mixed tensile-shear crack, and indirect crack coalescence. Coalescence through tensile linkage occurred mostly at pre-peak stress. In contrast, coalescence through shear or mixed tensile-shear cracks occurred at higher stress. Overall, this study indicates that the geometry of preexisting flaws affect crack initiation and coalescence behaviour. Keywords Crack coalescence Moulded gypsum Non-parallel flaws Primary cracks Uniaxial compression test B Lekan Olatayo Afolagboye afotayour@hotmail.co.uk 1 Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing , China 2 University of Chinese Academy of Sciences, Beijing , China 1 Introduction Rock masses contain a series of microcracks and fissures that are randomly oriented and observed at different scales. The microcracks and fissures that are present in a natural rock mass govern the mechanical behaviour of rock mass [1,2]. Failure or deformation of rock mass subjected to compressive loads occurs from initiation, propagation, and linkage of cracks, through the rock bridge, and from preexisting microcracks and fissures [3 8]. Therefore, it is vital to understand the mechanical properties, crack propagation, and coalescence behaviour of discontinuities in a rock mass to predict the failure process and ensure the integrity or stability of rock engineering structures [9 11]. Over the last decade, a series of experimental and numerical investigations have been conducted to understand the cracking process of rock masses. These investigations include observation of the crack initiation, interaction, propagation, and subsequent coalescence of natural rocks and rock-like materials containing single or multiple preexisting flaws under compressive loading [11 31]. Such factors as configuration or geometries [12,16,17,21,24,32], and properties (closed, opened, or three-dimensional) of preexisting flaws [24,28,29] influence crack propagation and the coalescence process. Most aforementioned investigations focused on rock or rock-like specimens with open or closed parallel flaws arranged in a co-planar or stepped format because joints often occur in sets that are parallel to each other. However, in nature, a rock mass may consist of a joint system of two or more joint sets, which can lead to coalescence between flaws of different orientations. Lee and Jeon [17] conducted a series of uniaxial compression tests on polymethyl methacrylate (PMMA), Diastone, and Hwangdeung granite to study the coalescence behaviour

2 Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping of two non-parallel flaws consisting of a horizontal flaw and an underlying inclined flaw. The inclination angle of the flaw varied between 30 and 90, while the ligament length and angle were constant. The authors reported little difference in the crack initiation and propagation pattern in the samples. Tensile and shear cracks were observed in Diastone and Hwangdeung granite, though tensile cracks occurred before shear cracks; only tensile cracks were observed in the PMMA specimens. In addition, most of the coalescence observed in the study was through tensile crack linkage. Yang et al. [25] performed uniaxial compression tests on red sandstone containing two non-parallel flaws where the inclination angle of one flaw was fixed at 45 and the other varied. The authors investigated the influence of the flaw orientations on the strength and deformation behaviour of red sandstone. They examined the crack coalescence process in the red sandstone under uniaxial compression by using photographic and acoustic emission (AE) monitoring techniques. The authors concluded that the peak strength and nature of coalescence depended on the flaw geometry and heterogeneity of rock material. This physical experiment was repeated numerically by Yang et al. [26] in a study using discrete element model. The strength, failure mode, and coalescence pattern were all in agreement with the experimental results. Huang et al. [31] conducted a series of uniaxial compression tests on rock like material to study the effect of preexisting fissures on mechanical properties and coalescence process. Similar to the work of Lee and Jeon [17], the fissures consist of a horizontal flaw and an underlying inclined flaw. The inclination angle of the flaw, however, varied between 0 and 75, while the ligament length was constant. The crack initiation and coalescence pattern were all in agreement with the prior experimental results of Lee and Jeon [17]. These previous studies have provided a good baseline for understanding the cracking process and coalescence behaviour between non-parallel flaws. However, few studies exist on non-parallel flaws, and among these studies the geometries of the flaws are designed to have different inclination angles. The cracking process of rock masses with two sets of non-parallel fractures can be predicted with a more thorough understanding of the cracking process between the various possible combinations of non-parallel flaws. To increase the understanding of the cracking process between non-parallel flaws, it is necessary to study cases where the flaw geometry consists of two flaws with equal inclination angles that are directly beneath each other. In this study, we observed crack propagation and coalescence between two non-parallel flaws with equal inclination angles that were directly beneath each other. This geometry was expected to give insight into understanding the cracking mechanism and process in a rock mass with different discontinuous joint sets consisting of high and low dip angles, as shown in Fig. 1 [33]. Fig. 1 Conceptual rock mass diagram of non-parallel joints. Adapted from Huang et al. [33] 2 Experimental studies Unconfined compression tests (UCTs) were conducted on a prismatic moulded gypsum specimen with two open nonparallel flaws (12.7 mm long with an aperture of 1.27 mm). Table 1 shows the properties of the gypsum specimen. The dimension (Fig. 2a) of the specimen (152 mm (height) 76 mm (width) 32 mm (thickness)) and sample preparations generally follow the procedures used in previous experimental studies [12,34]. The moulded gypsum specimens were produced from a mixture of water, celite, and high-strength gypsum powder produced by the Beijing Institute of Building Research at ratios of 600:210:2. The mixture was thoroughly blended and poured into a steel mould. The non-parallel flaws were made in the specimen by inserting metal shims into the gypsum paste. The metal shims were removed when the paste hardened. Thereafter, the specimens were removed from the mould and placed in an oven at a temperature of 40 C. The specimens were removed from the oven when constant mass was attained. The flaw geometries are shown in Fig. 2b. The inclination angle (β) of the two flaws were equal and from 15 to 60 in 15 intervals. Ligament length (L) wassetat either a, 2a, or3a, where a is equal to half flaw length. Fifteen different flaw configurations were tested (Table 2) with at least three specimens tested for each flaw geometry. The UCTs were conducted with a servo-controlled testing system with a maximum loading capacity of 2000 kn and maximum displacement capacity of 30 mm. The specimens were loaded under a load-displacement controlled condition with loading rate set at 0.06 mm/s. A Sony DCR-HC65 video recorder was used to capture the entire loading process in real-time video. High-speed imagery/video of the specimen front face was taken using a PCO Dmax S-series high-speed camera that was controlled by computer.

3 396 L. O. Afolagboye, et al. Table 1 Mechanical properties of the moulded gypsum Properties Values (average of 10 samples) Uniaxial compressive strength (MPa) Young s modulus (GPa) 7.50 Uniaxial tensile strength (MPa) 5.34 Specific gravity 2.48 Dry density (g/cm 3 ) 2.20 Fig. 2 a The dimension of the gypsum specimen with the non-parallel flaws. b The flaw geometry showing the inclination angles (β),ligament angle (α), and ligament lengths (L) The high-speed camera was programmed to capture approximately images in eight seconds at a pixel resolution. The high-speed camera only captured the images during coalescence or specimen failure. A digital camera was used to take images before, during, and after the test, as well as at key events such as crack initiation, spalling, and failure. Stresses at which key events occurred were determined based on the load-displacement data. From the pictures and videos taken by the high-speed camera and Sony video recorder during the compression test, AutoCAD was used to visually present the cracking sequence and progression. 3 Results and discussion 3.1 Primary cracks Wong and Einstein [13] had earlier suggested that primary cracks should be used to indicate a temporal relationship that refers to all the first cracks that initiate. Zhang and Wong [16] termed the first crack or group of cracks that initiate simultaneously at low stress as primary cracks. Park and Bobet [28,29] observed that tensile wing cracks (TWCs) are often the first cracks to emanate from a preexisting flaw. These cracks originate from the tips or farther away from the flaw tip, depending on flaw inclination, and propagate in the direction of maximum stress. In almost all the flaw geometries tested, a coalescence tensile crack (inner wing crack) initiating from the inner tips of the flaws and TWCs (external wing cracks) initiating from the upper and lower face of the outer tips of the top and bottom flaws, appeared first. Both the external and internal wing cracks, irrespective of the flaw inclination angle, started near or at the flaw tips. The position of TWC initiation moved closer to the flaw tip as the flaw inclination angle increased. Figure 3 shows the primary cracks observed in some flaw geometries with their initiation positions. Only the external wing cracks grew towards the edges of the specimen and remained open up to coalescence or failure, but the aperture may be reduced. However, in specimen 2a-15-1, the aperture of the low external tensile crack closed completely. The external wing cracks always formed the failure plane of the specimens. The high-speed camera recordings showed that the coalescence tensile crack initiation process occurred as a sudden incident and consisted of a single crack that developed between the two flaws (close or at the inner tips). In geometries with a low β(15 and 30 ) and L 2a, the aperture of the primary coalescence tensile cracks reduced. In some instances, the crack aperture closed completely with further initiation and propagation of additional cracks from the inner or outer tips of the flaws. Figure 4a d depicts this observation in one of the specimens (3a-15). The primary cracks initiated at similar stress state regardless of the tip or flaw from which they initiated. The initiation stress of the primary cracks decreased with reduced flaw Table 2 Number of specimens of the gypsum specimens and flaw configurations Angle of inclination (β ) Ligament angle (α ) Ligament length (mm) a 2a 3a a-15 2a-15 3a a-30 2a-30 3a a-45 2a-45 3a a-60 2a-60 3a-60 Note: a is equal to half flaw length. Specimen with configuration 3a-60 indicates that L = 3a and β = 60

4 Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping Fig. 3 Primary cracks observed in some geometries. a β = 15. b β = 45 inclination angles. Figure 5 shows the relationship between the primary crack initiation stress and flaw inclination angles. From the figure, geometries with a flaw inclination of 15 have the lowest primary crack initiation stress. In all inclination angles, the initiation stress of primary cracks in specimens with a ligament length of a were lower than the initiation stress of specimens having ligament lengths of 2a or 3a. There was little change in initiation position of TWCs with the increasing ligament length. 3.2 Secondary cracks Secondary cracks are cracks that appear after primary cracks and initiate from the tips of the flaws. Wong and Einstein [13] noted that different types of cracks could initiate after the initiation of primary cracks. Continuous increase in load led to the appearance of secondary cracks. At the same time, the initial external TWCs propagated further and were sometimes accompanied by an increase or decrease in the aperture of the primary cracks. The secondary cracks observed in this work were not limited to shear cracks but also included tensile or mixed tensile-shear cracks. The secondary cracks typically caused additional coalescence between the flaws, but in certain cases, they did not participate in coalescence. The secondary cracks could initiate from both the outer and inner tips of the flaw although the stresses at which the secondary cracks initiated from the flaw tips were different. On some flaw tips, more than one secondary crack and single primary crack may be observed, but in most cases only one single primary and secondary crack were observed. However, some flaw tips only had primary cracks. Gypsum powder was observed in the aperture of the flaws during the test. According to the observation by Bobet and Einstein [35], generation of gypsum powder is a sign of shear crack development around a flaw. The occurrence of a shear crack is always associated with surface spalling. Additional secondary tensile cracks, which were confined to the ligament area, linked the two tips together. The cracks initiated close to or at the tips of the inner flaws. In some configurations, propagation of this tensile crack led to the reduction or closure in the aperture of the primary coalescence tensile crack, linking the inner flaws. However, in configurations such as 2a-60-3, the disappearance of the initial tensile crack was due to the tensile crack that initiated from the lower face of the outer tip of the upper flaw. 3.3 Sequence of crack initiation and nature of coalescence cracks The sequence of crack initiation and nature of all new cracks that initiated from preexisting flaws observed in all of the gypsum specimens are shown in the sketches presented in Tables 3, 4, 5, and 6. To avoid duplication, only the sequence of crack development and coalescence of specimens with ligament length 3a, and specimens with β = 45 from geometries with ligament length 2a are described here. Each new crack is followed by a letter T or S and a number in subscript next to the letters. These letters indicate a tensile (T) or shear (S) mode of crack initiation, while the number indicates the sequence of crack initiation. New cracks that initiated simultaneously are given the same number. A crack that is represented by a dotted line indicates its aperture was completely closed by the end of the test. The cracks identified in this work are classified and named according to the scheme presented by Wong and Einstein [13].

5 398 L. O. Afolagboye, et al. Fig. 4 Pictures from high-speed camera illustrating the closure of the aperture of coalescence tensile crack as result of initiation of additional crack from the inner tips of the flaws. a Initiation of TWCs and coalescence tensile crack. b Initiation of additional tensile crack from the inner tips of the flaw. c Propagation of the tensile crack leading to gradual reduction in the aperture of the coalescence tensile crack. d The aperture of the coalescence tensile crack has closed completely Sequence of crack initiation of specimen with ligament length 3a β = 60 The primary cracks are the TWCs from the upper and lower face of the top and bottom flaws, and the coalescence tensile crack, which linked the internal tip of the flaws. The wing cracks originated close to or at the outer tip of the flaws and tended to propagate along the loading axis. As the load increased, additional cracks such as the tensile crack and mixed tensile-shear cracks, mostly from the top flaw, initiated from the flaw tips. A portion of these cracks were not involved in coalescence (TS 3 Specimen 1, TS 6,T 3,T 4 Specimen 2, TS 3,T 4 Specimen 3), and they all propagated in the direction of maximum stress (Table 3). Apart from the coalescence tensile crack that occurred before peak stress, other coalescence cracks were also observed in the specimens linking the two inner tips. The second coalescence crack consisted of a mixed tensile-shear crack in all specimens. The coalescence crack segments consisted of S-T-S in Specimens 1 and 2 and S-T in Specimen 3. The coalescence in Specimens 2 and 3 occurred at post-peak stress. In contrast, coalescence occurred during the peak stress in Specimen 1. β = 45 The first cracks to initiate were the TWCs and coalescence tensile crack. The TWCs in all specimens initiated close to or at the outer tips of the preexisting flaws at both the upper face of the top flaw and the lower face of the bottom flaw. The coalescence tensile crack linked the two flaws close to the inner tip of the flaws. Additional cracks initiated at a later stage of loading from both the inner and outer tips of the flaws (Table 4). Similar to specimens with a flaw inclination of 60, other coalescence cracks, apart from the primary tensile coalescence crack, were observed at the bridging area linking the two inner tips of the flaws. The coalescence was post-peak achieved by a single mixed tensile-shear crack in

6 Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping Fig. 5 Relationship between the primary crack initiation stress and flaw inclination angle for all the geometries Specimen 1 (S-T-S) and Specimen 2 (S-T). The coalescence occurred at peak stress in Specimen 3 and consisted of a tensile crack. Only Specimen 1 developed an additional postpeak coalescence (crack TS 3 ) at the left tip of the flaws. The coalescence was achieved by a single mixed tensile-shear crack (S-T-S), linking the outer tips of the two flaws. β = 30 The first cracks to initiate were also the TWCs and coalescence tensile crack. The external TWCs in all specimens initiated close to the outer tip of the flaws and from the upper and lower face of the top and bottom flaws. The coalescence tensile crack linked the two flaws close to or at the tip of the inner flaws (Table 5). In contrast to Specimen 2, the coalescence at the inner tip of the flaws in Specimen 1 and 3 was not restricted to the primary coalescence tensile crack. The other coalescence in Specimen 1 was achieved by a direct shear crack (crack S 3 ), linking the two inner tips at peak stress. The coalescence in Specimen 3 was a post-peak indirect coalescence achieved through a tensile crack that initiated from the inner tip of the upper flaw, and a mixed tensile-shear crack that initiated from the lower face of the inner tip of the lower flaw. Additional coalescence (Specimens 1 and 2) at the left tip of the flaws consisted of a single mixed tensile-shear that linked the two flaws tips. The cracks initiated from the upper flaw and linked the lower flaw after peak stress. β= 15 TWCs from the upper and lower face of the top and bottom flaw, respectively, and the coalescence tensile crack occurred first. The external wing cracks originated slightly farther away from the flaw tips and propagated along the loading axis. Other tensile cracks and mixed tensile-shear cracks also developed from the preexisting flaw tips (Table 6). With continuous increase in load, initiation of other cracks led to coalescence that resulted in the closure of the primary coalescence tensile crack, for example, initiation of the mixed tensile-shear crack (TS 2 ) in Specimen 1 and tensile crack (T 2 ) in Specimen 3. The closure of the tensile crack coalescence in Specimen 2 occurred due to further propagation of the mixed tensile-shear crack (TS 5 ) during failure of the specimen. With the exception of Specimens 1 and 2, the first crack coalescence occurred in the bridging region and was achieved through a tensile linkage (T 2 ) in Specimen 3. This coalescence crack linked the inner tips of the two flaws and occurred before peak stress was attained. However, in Specimens 1 and 2, cracks (T 3 and TS 5 in Specimen 1 and T 4 in Specimen 2) similar to those responsible for coalescence in Specimen 3 developed, but they did not propagate far enough to reach the other flaw for coalescence. The following additional post-peak coalescence developed at the left tip of the flaws in the specimens. In Specimens 1 and 3, direct coalescence cracks linked the left tips of the top and bottom flaws. These cracks (TS 2 in Specimen 1 and TS 4 in Specimen 3) consisted of mixed tensile-shear (TS) cracks. Specimen 1 also developed an additional tensile crack coalescence, linking the left tip of the upper flaw and the face of the lower flaw. In Specimen 2, indirect coalescence involved a mixed tensile-shear crack (TS 5 ) originating from the left tip of the upper flaw and a tensile crack (T 3 ) originating from the left tip of the lower flaw Sequence of crack initiation of specimen with ligament length 2a β = 45 The initiation of primary cracks was different among the specimens tested (Table 4). In Specimens 1 and 3, the primary cracks were the TWCs and coalescence tensile crack. The external TWCs, both from the upper and lower face of the top and bottom flaw, initiated close to the flaw tips and propagated towards the specimen edge. In Specimen 3, however, the external TWC only initiated from the upper face of the top flaw. The primary coalescence crack in the two specimens linked the tips of the inner flaw together. In Specimen 2, a TWC at the upper face of the top flaw occurred first, followed by a mixed tensile-shear crack (TS 2 ) at the upper face (left tip) of the lower flaw. Additional cracks, such as mixed tensile-shear and shear cracks, initiated at a later stage of loading from both the inner and outer tips of the flaws. Some of these cracks were involved in coalescence (TS 2 Specimen 1, T 4 Specimen 2, S 4 Specimen 3). Those cracks not involved in coalescence propagated in the direction of maximum stress. The coalescence at the ligament area in Specimens 1 and 2 was achieved by a tensile crack linking the two inner tips of the flaws. Although the coalescence occurred before the peak stress, the coalescence crack in Specimen 1 consisted of the primary coalescence tensile crack. In Specimen 3, the coalescence consisted of a

7 400 L. O. Afolagboye, et al. Table 3 Sketches of sequence of crack initiation and the nature of coalescence pattern in specimens with β = 60 primary coalescence tensile crack linking the two inner tips, an indirect coalescence involving a shear crack (S 4 ) from the inner tip of the top flaw, and mixed tensile-shear (TS 2 ) crack from the inner tip of the lower flaw. The direct and indirect coalescence occurred at pre-peak and post-peak stress, respectively. Only Specimen 1 recorded an additional postpeak stress coalescence at the left tip of the flaws, which consisted of a single mixed tensile-shear that linked the two flaw tips. Specimens 2 and 3 also had mixed tensile-shear cracks similar to the crack responsible for the coalescence in Specimen 1, but they did not propagate far enough to reach the other flaw for coalescence.

8 Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping Table 4 Sketches of sequence of crack initiation and the nature of coalescence pattern in specimens with β = Nature of coalescence cracks Many different crack coalescence classifications based on the coalescence between two parallel flaws are available in the literature. Proper identification of the nature of the coalescence crack(s) drives the different classifications. Bobet and Einstein [35] identified the coalescence cracks as either tensile or shear cracks and based on the combinations of these cracks, they identified five coalescence patterns. Wong and Chau [32] categorised the coalescence patterns into nine types. Sagong and Bobet [14] identified three coalescence cracks tensile crack, quasi-coplanar shear crack, and

9 402 L. O. Afolagboye, et al. Table 5 Sketches of sequence of crack initiation and the nature of coalescence pattern in specimens with β = 30 oblique shear crack and came up with nine different coalescence patterns. Wong and Einstein [12] presented nine crack coalescence classifications based on the nature and trajectory of cracks identified by Wong and Einstein [13] usingahigh speed camera. Table 7 summarises the nature of coalescence crack(s) observed for each specimen of the different geometries in our experimental studies. The nature of coalescence cracks observed includes a primary coalescence tensile crack, tensile crack linkage, shear crack linkage, and a mix of both

10 Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping Table 6 Sketches of sequence of crack initiation and the nature of coalescence pattern in specimens with β = 15 tensile and shear crack segments. The coalescence can be achieved through either a direct or indirect linkage. Wong and Einstein [12] provided the definition of direct and indirect coalescence for coalescence involving two flaw tips. Additionally, apart from the primary coalescence tensile crack, coalescence cracks can occur in the bridging area (right tip of the flaws) and left tip of the flaws. The stress at which the coalescence occurred could be pre-peak, at-peak or post-peak stress (Table 7). Coalescence achieved through tensile linkage mostly occurred before the peak stress, which indicated

11 404 L. O. Afolagboye, et al. Table 7 Nature of coalescence cracks observed in each geometries Inclination angle ID L = a L = 2a L = 3a 60 1 CT 1,M 2 T 1 CT 1,M 2 2 CT 1,T 1, CT 1 CT 1,M 3 3 CT 1,T 1 CT 1 CT 1,M CT 1,T 1,M 3L CT 1,M 3L CT 1,M 3,M 3L 2 CT 1,T 1,M 2L CT 1 CT 1,M 3 3 CT 1,T 1,M 2L CT 1,I 3 CT 1,T CT 1,T 1,M 2L CT 1,T 1 CT 1,S 3,M 3L 2 CT 1,M 2,S 3L CT 1,T 1,I 2,M 3L CT 1,M 3L 3 CT 1,T 1,M 2L CT 1,T 1 CT 1,I CT 1,T 1,M 3L CT 1,T 1, No, M 3L,T 3L 2 CT 1,I 3,M 3L CT 1,M 2,M 3L No, I 3L,T 3L 3 CT 1,T 1,M 2L T 1,M 3L T 1,M 3L Note: CT: coalescence tensile crack, T: tensile crack linkage, S: shear crack linkage, M: mixed tensile-shear crack linkage, I: indirect coalescence, No: no coalescence, L: coalescence at the left side of the flaws, 1: pre-peak stress, 2: peak stress, 3: post-peak stress that this type of coalescence is easily achieved. An example is coalescence through the primary tensile coalescence crack in which further loading of the specimen was needed to record another coalescence or reach the peak stress. Coalescence through shear or mixed tensile-shear linkage tends to occur at peak or post-peak stress. At the bridge area, the coalescence crack could be tensile crack linkage, shear crack linkage, or mixed tensile shear cracks and may not be limited to a single crack type. In almost all of the flaw geometries with ligament length a, the coalescence occurs mainly through direct tensile linkage, with the exception of specimens a-60-2, a-30-2, and a-15-2 (Table 7). The direct coalescence cracks consisted of both the primary coalescence tensile crack and additional tensile cracks developed during the latter stages of loading. In specimens with ligament length 2a, the coalescence varied between tensile cracks, mixed tensile-shear crack, and indirect cracks linkage as flaw inclination changed. A high inclination angle (60,45 ), however, favoured a single crack coalescence involving only the primary coalescence tensile crack. Specimens with a flaw inclination of 30 and 15 achieved second coalescence, apart from the primary tensile crack coalescence. In specimens with ligament length 3a, the coalescence varied between tensile cracks, mixed tensileshear crack, indirect cracks linkage, and no coalescence as flaw inclination changed. In all of the flaw geometries with L = 3a, all specimens, except for β = 15, achieved two coalescences at the bridging area. In geometries with a flaw inclination of 15, larger ligament length between the inner tips of the flaw reduced the probability of coalescence in these flaw geometries. Geometries a-15 and 2a-15 showed either indirect or direct coalescence, but no coalescence was achieved in 3a-15. Mixed tensile shear-cracks accounted for most of the coalescence cracks at the left tips of the flaws. Coalescence behaviour at the left side of the flaw varied slightly with flaw inclination angle (β). For specimens with a high inclination angle (60 ) at all ligament lengths, no coalescence cracks developed at the left tips of the flaws. When the ligament length was 2a, only one specimen among all specimens with inclination angles of 45 and 30 demonstrated coalescence. With ligament length equalling 3a, one specimen recorded coalescence when the flaw inclination was 45, and two specimens recorded coalescence cracks when the flaw inclination was 30. In specimens with a low inclination angle (15 ), tensile crack linkage and indirect coalescence were recorded at the left tip of the flaws. 4 Conclusions In this study, we used a PCO high-speed camera to observe the cracking behaviour and coalescence between two nonparallel preexisting flaws that were directly beneath one another. The primary cracks were coalescence tensile crack and tensile wing cracks from the tips of the flaws. The initiation stresses of the primary cracks at the two tips of each flaw were simultaneous and decreased with a reduction in the flaw inclination angle. The following types of coalescence cracks were identified among the flaws: primary tensile coalescence cracks, tensile crack linkage, shear crack linkage, a mix of both tensile and shear crack segments, and indirect crack coalescence. Coalescence at the ligament area occurred mostly through tensile linkage and before the peak stress. Coalescence through shear or mixed tensile-shear linkage tended to occur at peak or post-peak stress. Larger ligament length

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