Mode I Critical Stress Intensity Factor of Medium-Density Fiberboard Obtained by Single-Edge-Notched Bending Test

The Mode I critical stress intensity factor (KIc ) obtained by single-edge-notched bending (SENB) tests of medium-density fi berboard (MDF) was experimentally analyzed. In the SENB test, the critical load for crack propagation (Pc ) was determined from the relationship between load/loading-line displacement and load/crack opening displacement (COD). A double cantilever beam (DCB) test was also conducted and the results were compared with those of SENB tests. The value of Mode I critical stress intensity factor was obtained by introducing an additional crack length, when the crack length ranged from 0.5 to 0.7 times the depth of the specimen. This range coincided well with that used to derive the appropriate KIc value in the single-edge-notched tension (SENT) test, which was conducted using the specimens with a similar confi guration cut from the MDF panel used in this study.


INTRODUCTION 1. UVOD
In analyzing the fracture behavior of material based on fracture mechanics theory, the value of critical stress intensity factor K c is often measured because it can be regarded as a material constant.Of the three independent fracture modes, the crack opening mode (Mode I) is regarded as more important than the inplane shear mode (Mode II) and out-of-plane shear mode (Mode III) because the Mode I critical stress intensity factor (K Ic ) is usually smaller than those of Mode II and Mode III, K IIc and K IIIc , respectively.To determine the K Ic value, single-edge-notched bending (SENB), single-edge-notched tension (SENT), compact tension (CT), and double cantilever beam (DCB) tests, the diagrams of which are shown in Figures 1(a)-(d), respectively, are most frequently performed because the crack propagation under the opening mode can be easily induced by these tests.
In previous works, the K Ic value of medium-density fi berboard (MDF) was examined by SENT and CT tests (Yoshihara, 2010b;Yoshihara and Usuki, 2011).In these tests, we found that the K Ic value of MDF can be effectively measured when considering the additional crack length ahead of the crack tip and restricting the range of initial crack length with respect to the specimen geometry.Nevertheless, these tests require attachments to apply the tensile load, so the use of the attachments often restricts the specimen geometry.The SENB test is attractive because it can be conducted using specimens with various geometries more easily than the SENT and CT tests (Yoshihara, 2010a).
In this study, we examined the K Ic value of MDF by the SENB test using two types of specimens with different dimensions.The results were compared with those obtained from the DCB tests, which can be determined based on energy consideration and are mathematically well defi ned (Adams et al., 2003).

Materijali
An MDF panel, which was used in previous works (Yoshihara, 2010b; Yoshihara and Usuki, 2011), was investigated.The density of the MDF at 12 % moisture content (MC) was 580 ± 10 kg/m 3 .The panel was stored in a room at a constant 20 °C and 65 % relative humidity (RH) before the test, and the specimens were confi rmed to be in an air-dried state.These conditions were maintained throughout the tests.Five specimens were tested for each test condition.Two kinds of specimens were tested.Specimen A had dimensions of 20 × 90 × 15 mm 3 , while these dimensions were 40 × 180 × 15 mm 3 in specimen B. The specimen depth W was 20 and 40 mm in specimens A and B, respectively.The crack was fi rst cut with a band saw (thickness = 1 mm) and then extended 1 mm ahead of the crack tip with a razor blade.The crack length a varied from 1 to 18 mm at intervals of 1 mm in specimen A, and from 2 to 36 mm at intervals of 2 mm in specimen B. Thus, the value of a/W varied from 0.1 to 0.9 at intervals of 0.1.The specimen confi gurations were similar with those of SENB tests for western hemlock (Yoshihara, 2010a).
In the SENB test of western hemlock, the nonlinearity in the relationship between the load (P) and loading-line defl ection (δ) was not signifi cant until the init iation of crack propagation, so the critical load for crack propagation was determined as the maximum load (Yoshihara, 2010a).From the results of the SENT and CT tests of MDF in which the crack opening displacement (COD) was measured, the nonlinearity was marked in the P-COD relationship (Yoshihara, 2010b; Yoshihara and Usuki, 2011).Although the loading-line displacement in the SENB test is signifi cantly larger than that in the SENT and CT tests, we thought that the measurement of the COD was effective to detect the nonlinearity and δ.To measure the COD, a clip gauge extensometer (capacity = 5 mm; UB-5, Tokyo Sokki, Co., Tokyo, Japan) was used.The specimen was symmetrically supported and loaded at the mid-span.The span lengths (L) were 80 and 160 mm in specimens A and B, respectively, giving an L/W value of 4. A steel platen was placed between the specimen and the support to reduce indentation at the supporting point.The load P was applied at a crosshead speed of 0.5 mm/ min 1 until the load markedly decreased.The total testing time was approximately 5 min.
Figure 2 shows typical P-δ and P-COD relationships obtained by the SENB tests.In the results for western hemlock, the crack often propagates unstably when the initial crack length is less than 0.3 times the depth of the specimen, whereas it propagates stably when the initial crack is longer than 0.4 times the depth (Yoshihara, 2010a).In the results of MDF, however, the crack always propagates stably all over the range of the initial crack length.In addition, the P-δ and P-COD relationships were signifi cantly nonlinear before the load reached its maximum.Therefore, the critical load for crack propagation P c was provisionally determined to be the load at the onset of nonlinearity.This was determined in the same manner as that used for the SENT and CT tests (Yoshihara, 2010b; Yoshihara and Usuki, 2011) and for the DCB tests described below.
Similar to the previous investigation (Yoshihara 2010a), the K Ic value was initially evaluated using the following two equations, which were originally proposed by Gross and Srawley (1965) and Srawley (1976): The K Ic value was measured by the DCB test using a side-grooved specimen independent of the SENB test, and it was compared with those obtained from the SENB test.The details of the DCB test were similar to those previously conducted (Yoshihara, 2010a, b).

REZULTATI I RASPRAVA
Figure 3 shows the K Ic -a/W relationships obtained from the SENB tests using Eqs.( 1) and ( 2) and a comparison of these relationships with the results obtained by the DCB tests.A convex trend was identifi ed in these relationships.This trend is different from that obtained by the SENB tests of western hemlock.That trend was almost constant in the a/W range of 0.1-0.7 and 0.1-0.9 when using Eqs.( 1) and ( 2), respectively (Yoshihara, 2010a).The K Ic value obtained from specimen A is larger than that from specimen B when com-paring the same a/W value, except for a/W = 0.1, so the K Ic values obtained from Eqs. ( 1) and ( 2) are regarded to be dependent on the specimen geometry.The point at the onset of nonlinearity, the load at which it was provisionally defi ned as the critical load for crack propagation P c , could be found earlier in the P-COD relationship than in the P-δ relationship.Therefore, the K Ic value obtained from the P-COD relationship is smaller than that obtained from the P-δ relationship.
Figure 3 suggests that the K Ic values obtained using Eq. ( 1) and ( 2) are defi nitively smaller than that obtained by the DCB test because the development of a softened region ahead of the crack tip, such as fracture process zone (FPZ), is not taken into account in these equations.Due to the softened region, the cracked specimen often behaves as if the crack were longer than the actual length.Similar to the approach adopted in previous investigations (Yoshihara, 2010a, b; Yoshihara and Usuki, 2011), the relationship between K Ic and a is modifi ed by introducing an additional crack length ∆ into Eqs.( 1) and ( 2) as follows: (3) and ( 4) (Yoshihara 2010b).Therefore, the K Ic values for a/W values smaller than 0.4 were measured to be smaller than those in the a/W range from 0.5 to 0.7.In contrast, the value of K Ic calculated from Eq. ( 3) decreases in the a/W range larger than 0.8, whereas that calculated from Eq. ( 4) diverges when a/W exceeds 0.8 because the value of 1 -(a + ∆)/W contained in the equation is close to zero.Therefore, the K Ic -a/W relationships obtained from Eqs. ( 3) and ( 4) are extremely different from each other when the value of a/W exceeds 0.8.Additionally, when the crack tip is close to the loading point, the compressive stresses due to the indentation of the loading nose hinder self-similar crack propagation (de Moura et al., 2010).From these reasons, the appropriate range for introducing the additional crack is restricted.From the results obtained here, the K Ic value should be measured using Eq. ( 3) in the a/W range from 0.5 to 0.7.
In this research, the additional crack length ∆ is determined by statistically comparing the K Ic values obtained from the P-δ and P-COD relationships and that obtained by the DCB test.Therefore, the ∆ value is dependent on the relationship used in the analysis, as shown in Table 1.Based on the concept of the FPZ, however, the value of ∆ can be physically obtained (Vasic and Smith, 2002; Vasic et al., 2003;Morel et al., 2003;2005;de Moura et al., 2008de Moura et al., , 2010;;Dourado et al., 2008Dourado et al., , 2010)).As shown in Figure 2, the K Ic values obtained from both P-δ and P-COD relationships are similar to each other when correcting the crack length.Therefore, it is diffi cult to determine which relationship is more valid for determining the K Ic value.Microscopic observation (Vasic and Smith, 2002;Vasic et al., 2003) and digital image correlation observation (Murata et al., 2011) around the crack tip during loading may be effective to reveal the validity of the relationships.
According to the research on the Mode II critical stress intensity factor K IIc of wood and MDF as determined by an asymmetric four-point bending test, the K IIc value can be obtained by introducing the additional crack length when a/W exceeds 0.8, when an appropriate equation is derived for the crack geometry factor (Yoshihara submitted).In the SENB tests of solid wood (Yoshihara, 2010a) and MDF, two previously proposed equations (Eqs.( 1) and ( 2)) were used and modifi ed by considering the additional crack length.Further research should be conducted to fi nd a new equation that can derive the K Ic value properly for the specimen with an a/W value larger than 0.8.In addition, the compressive stresses due to the indentation of the loading nose The appropriate value of additional crack length ∆ was determined from the following procedure, which was similar to those conducted in previous studies (Yoshihara, 2010a, 1 are longer than those of western hemlock, which were 2 and 4 mm for specimen A and B, respectively (Yoshihara, 2010a).The ∆ value obtained from the P-COD relationship is larger than that obtained from the P-δ relationship.Figure 3 also shows the results calculated by Eqs.
(3) and ( 4).The values of K Ic obtained from Eq. ( 3) are close to those obtained by the DCB tests when a/W falls in the approximate range of 0.5 to 0.7.A statistical analysis of the difference between the K Ic values obtained using the SENB and DCB tests shows that the difference is not signifi cant in this a/W range, regardless of whether the P c value is determined from the P-δ or P-COD relationship.This range coincides well with the range used to derive the appropriate K Ic value in the SENT test (Yoshihara 2010b).When using Eq. ( 4), however, the applicable range of a/W is narrower than that obtained using Eq. ( 3).When the a/W value is smaller than 0.4, material nonlinearity precedes the crack propagation, so the load at the onset of nonlinearity in the P-δ and P-COD relationships P c cannot be regarded as the critical load for crack propagation

Figure 1 (
Figure 1(a) shows the diagram of the SENB test.Two kinds of specimens were tested.Specimen A had dimensions of 20 × 90 × 15 mm 3 , while these dimensions were 40 × 180 × 15 mm 3 in specimen B. The specimen depth W was 20 and 40 mm in specimens A and B, respectively.The crack was fi rst cut with a band saw (thickness = 1 mm) and then extended 1 mm ahead of the crack tip with a razor blade.The crack length a varied from 1 to 18 mm at intervals of 1 mm in specimen A, and from 2 to 36 mm at intervals of 2 mm in specimen B. Thus, the value of a/W varied from 0.1 to 0.9 at intervals of 0.1.The specimen confi gurations were similar with those of SENB tests for western hemlock(Yoshihara, 2010a).In the SENB test of western hemlock, the nonlinearity in the relationship between the load (P) and loading-line defl ection (δ) was not signifi cant until the init iation of crack propagation, so the critical load for crack propagation was determined as the maximum load(Yoshihara, 2010a).From the results of the SENT and CT tests of MDF in which the crack opening displacement (COD) was measured, the nonlinearity was marked in the P-COD relationship (Yoshihara, 2010b; Yoshihara and Usuki, 2011).Although the loading-line displacement in the SENB test is signifi cantly larger than that in the SENT and CT tests, we thought that the measurement of the COD was effective to detect the nonlinearity and δ.To measure the COD, a clip gauge

9 Figure 2 2 .
Figure 2Typical example of the relationship between load P and loading-line displacement δ and that between P and the crack opening displacement COD for various crack lengths a in SENB test.Depth of the specimen W = 40 mm Slika 2. Tipičan primjer odnosa između opterećenja P i pomaka linije opterećenja δ te između opterećenja P i širenja pukotine COD za različite duljine pukotine a u SENB testu; debljina uzorka W = 40 mm

Figure 3
Figure 3 Comparison of the relationships between K Ic and a/W obtained by SENB test and that obtained by DCB test Slika 3. Usporedba odnosa između K Ic i a/W dobivenoga SENB testom i DCB testom b;Yoshihara and Usuki, 2011).By altering the value of ∆, the probability value (p-value) for the averages of KIc obtained by the SENB test corresponding to each a/W and DCB test is calculated by Student's t-test.Then the p-values corresponding to each ∆ are summed up.When the amount of the p-values is large, the average values of KIc obtained by the SENB and DCB tests can be regarded as being close to each other.The ∆ value was obtained by binary search algorithm as shown in Table1.The ∆ values listed in Table

Table 1
Additional crack length ∆ derived by statistically comparing K Ic values obtained from SENB and DCB tests (unit = mm)