Effect of temperature on the fracture toughness of wood under mode I quasi-static loading

Construction and Building Materials 223 (2019) 863–869

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Effect of temperature on the fracture toughness of wood under mode I quasi-static loading N. Dourado a,⇑, M.F.S.F. de Moura b a b

CMEMS-UMinho, Departamento de Engenharia Mecânica, Universidade do Minho, Campus de Azurém, 4804-533 Guimarães, Portugal Faculdade de Engenharia da Universidade do Porto, Departamento de Engenharia Mecânica, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


Mode I fracture characterization of

Pinus pinaster Ait. wood was analysed.
The influence of temperature on

fracture toughness was studied considering 9 values.
Non-negligible influence of toughness was observed for temperatures exceeding 90 °C.
Cohesive laws were determined to mimic the observed results for tested temperatures.

a r t i c l e

i n f o

Article history: Received 29 January 2019 Received in revised form 25 June 2019 Accepted 5 July 2019

Keywords: Wood Fracture characterization Mode I loading Temperature effect Cohesive zone modelling

a b s t r a c t A numerical and experimental study was performed to evaluate the critical strain energy release rate of wood under mode I loading (GIc), in the range of 30 °C and 110 °C. Pinus pinaster Ait. was employed as testing material, using the double cantilever beam (DCB) test, promoting fracture in the RL fracture system. The determination of Resistance-curves was accomplished using an equivalent crack length method, which does not require crack length measurement in the course of the experimental test. This aspect was found crucial since wood develops a non-negligible fracture process zone (FPZ) ahead of the crack tip, and the experiments required the use of a climate chamber with limited dimensions for visual access. It was observed that the critical energy release rate is affected by temperature within the referred range. Cohesive laws were also determined to replicate the experimental response as a function of the tested temperatures. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Given to its specific weight, wood presents a notable mechanical resistance and high fracture toughness [1]. However, similarly to other biological materials its mechanical properties are highly influenced by environmental conditions to which they are exposed, namely humidity [2,3] and temperature [4], as well as loading actions. The modifications that occur in the mechanical properties

⇑ Corresponding author. E-mail address: [email protected] (N. Dourado). https://doi.org/10.1016/j.conbuildmat.2019.07.036 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

of wood are due mainly to the degradation of hemicellulose, which is an important constituent of wood. In fact, the tensile strength and wood stiffness are governed by cellulose chains that degrade substantially for temperatures higher than 200 °C [5]. The compressive strength is mostly dictated by lignin, which becomes soft for temperatures around 100 °C but increases its hardness for higher temperatures [5]. Several studies reported in the literature refer that the increase of temperature in wood is responsible for the reduction of elastic properties, namely the bending strength and moduli of elasticity for the same water content [2,3]. Hamdi et al. [6] studied the effect of thermal loading coupled with

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Nomenclature a a0 ae B C C0 d D E EL GLR GI GIc GIb

Crack length Initial crack length Equivalent crack length Specimen thickness Specimen compliance Specimen initial compliance Damage parameter Damage parameter diagonal matrix Interface stiffness diagonal matrix Longitudinal elastic modulus Shear modulus in the LR plane Strain energy release rate under mode I loading Critical energy release rate under mode I loading Fracture energy under mode I loading due fibre-bridging

GIl h k P Pu d d0 db dap dr du to

viscoelastic effects in wood-based materials considering several mixed mode ratios. However, few studies have been performed aiming to assess the influence of temperature on wood fracture behaviour. Among the studies that address this issue, Reiterer [7] performed a study on the evaluation of the effect of temperature on wood (Picea abies L. and Fagus sylvatica L.) fracture properties in the RL fracture system under mode I loading using the wedge splitting test. The author considered four different values of temperature (20 °C, 40 °C, 60 °C and 80 °C), and verified, for both species, that toughness properties diminish with the increase of temperature. This author noticed that Fagus sylvatica L. shows higher toughness values, which was attributed to its higher density when compared to Picea abies L. Sinha et al. [8] analysed the influence of high temperatures on the mode I fracture properties of wood (Douglas fir species). The double cantilever beam (DCB) test specimens were exposed to two different temperatures (100 °C and 200 °C) for a period of one and two hours. The authors observed that this material is not affected by those conditions, with the exception of the most critical one, i.e., two hours at 200 °C, which induce a clear reduction of toughness. Murata et al. [9] analysed the effect of thermal treatment on fracture properties of wood Spruce. Specimens were heated at temperatures within the range 120–200 °C for 1 h and single-edge notched bending tests were performed to measure fracture energy under mode I loading. The authors observed an important decrease of fracture properties for temperatures over 150 °C, which is an indication that the chemical structure of the cell-wall is altered, owing to the fact that the fracture energy depends on cell-wall ultrastructure. In addition, Conrad et al. [10] argued that the increase of temperature intensifies viscoelastic deformation, leading to a shift from cell fracture to cell separation. This alteration of failure mode transforms the typical unstable crack extension that takes place in the case of cell fracture, into a stable crack growth characterizing cell separation. Tukiainen and Hughes [11] studied the effect of temperature and moisture content on the fracture behaviour of two wood species, spruce and birch. It was concluded that elevated temperatures significantly change the fracture behaviour of both species in RT and TR fracture systems. In both species, all the fracture mechanics parameters, except specific fracture energy, decreased with the increase of temperature or moisture content. However, the failure mode was not affected, with the exception of spruce in the RT fracture system. In this work, an experimental campaign aiming to characterize mode I fracture behaviour of wood (Pinus pinaster Ait.) under different temperatures was performed considering the DCB test. The

r rb ru

Fracture energy under mode I loading due to microcracking Specimen half-height Specimen initial stiffness Applied load Ultimate applied load Current relative displacement Onset relative displacement Relative displacement of inflection point Applied displacement Relative displacements vector Ultimate relative displacement Traction vector Traction at the inflection point Local strength

selected range (i.e., 30–110 °C) was chosen in order to assess the influence of high temperatures covering the structural applications of wood. The experimental Resistance-curves were obtained employing an equivalent crack length procedure circumventing the cumbersome and inaccurate crack length measurement task. The evaluation of the temperature influence of the Resistancecurves of wood is one of the relevant novelties of this study. A cohesive zone analysis considering a bilinear softening relationship was also performed in order to assess the influence of temperature on the parameters defining the cohesive law. 1.1. Objectives In summary, the main objectives of this work are to address the influence of temperature on wood (Pinus pinaster Ait.) fracture behavior in the range of 30°–110 °C. Therefore, the influence of temperature was analyzed on the following aspects: 1. The initial stiffness and ultimate load of the DCB specimen tests; 2. The critical strain energy release rate under mode I loading; 3. The cohesive law. 4. In addition, recommendations will be pursued to take into account the influence of temperature on wood structural applications. 2. Experimental testing 2.1. Mechanical tests Wood Pinus pinaster Ait. specimens were machined to comply with the longitudinal (L), radial (R) and tangential (T) anatomical

Fig. 1. Schematic representation of the DCB test.

N. Dourado, M.F.S.F. de Moura / Construction and Building Materials 223 (2019) 863–869

material orientations represented in Fig. 1. Adult wood was cut from thick and wide plank boards that have been in equilibrium with the lab environment (25 °C and 65% RH) for several months. Fibre saturation point of Pinus pinaster Ait. in used conditions was found on average at 28%. Machining operations were executed to produce specimens in clear wood (free from knots and resin pockets) with the grain well aligned with the longitudinal axis of the specimen. A total of 90 specimens were produced in these conditions, with the dimensions (see Fig. 1):2h ¼ 20, L ¼ 280, B ¼ 20 and a0 ¼ 130 (mm). Then, a hole (3.5 mm diameter) was executed in each specimen arm at the mid-height to apply the load (P) through a pair of metallic dowels connected to the testing machine. Subsequently, the specimens were left in the lab to attain the equilibrium moisture content for a period of one month. Following this period, specimens were randomly separated in 9 groups, to conduct individual fracture tests at a single temperature within the range of 30°–110 °C, with intervals of 10 °C. Prior to testing, each specimen sample was stored for a period of 12 consecutive hours inside an oven chamber to reach equilibrium. This acclimatization period inside the oven is higher than the ones measured by Manríquez and Moraes [12] and Young and Clancy [13], who employed thermocouples in the wood specimens for different dimensions and wood species. This procedure ensures the thermal stabilization that is required to accurately measure the influence of temperature on the whole wood sample. Once concluded the thermal stabilization period, the initial crack was produced in two consecutive steps: (a) band sawn (cut thickness of 1 mm) at the mid-height section for approximately 127 mm along the grain direction; and (b) by impact loading on a thin blade to mimic the propagation of a natural crack, thus totalizing the pretended extent (i.e., a0 ¼ 130 mm). Both notch and crack plan allowed undergoing tests in the RL fracture system of wood. Mode I fracture tests were executed inside a climate chamber (Fig. 2) attached to a servo-hydraulic testing machine (INSTRONÒ 8801) equipped with a load-cell of 5 kN. Preconditioned and crack-notched specimens were stabilized for a short period of time (15 min) inside this climate chamber to assure the attainment of the required temperature. Fracture tests were then executed under displacement control by choosing a crosshead velocity of 3.5 mm/ min. Load-displacement curves were recorded with an acquisition frequency of 5 Hz for each sample (30°110 °C) following this experimental protocol [14].

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2.2. Data reduction scheme As perceived in Fig. 2, the experimental tests were executed inside a climate chamber with quite limited visual access. In these circumstances, rigorous crack length checking during the DCB fracture test is an almost unmanageable task. In alternative, a previously developed equivalent crack length based procedure can be employed. The method depends on specimen compliance (C ¼ dap =P) which can be related with crack length by the following expression, determined through Timoshenko beam theory [14],

C¼

8a3 EL Bh

3

þ

12a 5BhGLR

ð1Þ

where EL and GLR are the material elastic properties, a the crack length and B and h specimen dimensions (Fig. 1). Since wood reveals an important scatter on its elastic properties, the longitudinal modulus is determined by means of an inverse procedure that consists in matching the numerical initial specimen stiffness to the one obtained experimentally, by iteratively altering the value of EL . This procedure is performed by setting the value of the crack a to a0 , since damage has not yet initiated. A nominal value is considered for the shear modulus GLR , owing to its negligible influence on the results. Aiming to increase the procedure accuracy, each specimen was analysed considering its real dimensions instead of the nominal ones. Consequently, the longitudinal modulus of each specimen is the value determined by the finite element analysis that allows reproducing the initial specimen stiffness obtained experimentally. The equivalent crack length ae as a function of the current compliance C, can be obtained from Eq. (1) using the MatlabÒ software [14]. Combining the Irwin-Kies equation

GI ¼

P 2 dC 2B da

ð2Þ

with Eq. (1) yields,

6P2

2a2e

1 GI ¼ 2 þ 2 5G LR B h EL h

! ð3Þ

This equation provides the evolution of the strain energy release rate (GI) as a function of the equivalent crack length (ae ), i.e., the Resistance-curve (R-curve), only using data ensuing from the load-displacement curve. This aspect is particularly relevant owing to limitations on the visual access to the specimen during the mechanical test. 3. Numerical approach

Fig. 2. Climate chamber and test setup of the DCB tests.

Finite element analysis (Fig. 3) for mode I fracture characterization of wood under different temperatures was performed considering cohesive zone modelling (CZM). A plane strain analysis was used considering 2300 isoparametric 8-node solid elements and a line of 111 compatible 6-node cohesive elements located at the specimen mid-height in the region of crack propagation. The mesh is more refined in this region, aiming to simulate damage progression accurately. A loading displacement of 20 mm was gradually applied with a small increment of 0.2%, aiming to induce numerical stable crack growth as observed experimentally. The elastic properties used in the simulations are listed in Table 1. The goal of the numerical analysis was to identify the influence of temperature on the main parameters defining the cohesive law representative of material fracture behaviour. Previous works [14,15] demonstrated that the trilinear cohesive law (CL) with bilinear softening relationship (Fig. 4) is appropriate to deal with wood fracture behaviour under mode I loading. In fact, wood reveals two different damage mechanisms ahead of the crack tip, e.g., micro-cracking and fibre bridging [15] that are well

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Fig. 3. Schematic representation of the finite mesh employed for DCB simulations.

Table 1 Wood (Pinus pinaster Ait.) elastic properties [16]. EL (GPa) 15.13 *

*

ER (MPa)

ET (MPa)

mLR

mLT

mRT

GLR (MPa)

GLT (MPa)

GRT (MPa)

1910

1010

0.471

0.509

0.585

1112

1040

170

This nominal value was not used; instead an inverse procedure described in Section 2.2 was followed to define EL for each specimen.

d¼

db ðd  d0 Þð1  /Þ ; dðdb  d0 Þ

d0  d  db

ð6Þ

with / ¼ ðrb d0 Þ=ðru db Þ. For the second softening branch the damage parameter becomes,

d¼1

/db ðdu  dÞ ; dðdu  d0 Þ

db  d  du

ð7Þ

being the ultimate displacement du given by the area circumscribed by the CL,

du ¼

2GIc þ rb d0  ru db

rb

ð8Þ

An inverse procedure was employed to identify the CL representative of the material fracture behaviour. The procedure consists in iterative adjustments of the CL altering the parameters db ; rb and ru aiming to get a good fit between the numerical and experimental load-displacement curves. Fig. 4. Schematic representation of the employed CL (GIc ¼ GIl þ GIb ).

4. Results and discussion

reproduced by the two softening branches of the CL. This fracture behaviour induces nonlinearity in the load-displacement curves reflecting energy dissipation in a non-negligible fracture process zone (FPZ). The first branch of the CL ð0  d  d0 Þ is representative of the linear elastic material behaviour characterised by the following relation,

r ¼ Edr

ð4Þ

where r and dr represent the traction and relative displacements vectors and E is a diagonal matrix containing the interface stiffness, respectively. This scalar (known as the penalty parameter) should be the highest possible in order to diminish unwanted interpenetrations under compression loading and, simultaneously, avoid numerical problems. In general, a value in the range 106–107 [N/mm3] is appropriate to satisfy these requirements. Once the local strength (ru ) is attained, the softening relation becomes,

r ¼ ðI  DÞEdr

ð5Þ

being I the identity matrix, and D a diagonal matrix containing the damage parameter, d, which depends on the softening branch of the law. In the first one, ðd0  d  db Þ the damage parameter yields,

The set of nine temperatures considered in this study (i.e., in the range: 30–110 °C with an interval of 10 °C) were treated separately. Fig. 5(a) and (b) show two examples of load-displacement and respective R-curves corresponding to the extreme values of the tested temperatures, 30 °C and 110 °C, respectively. These curves were chosen since they are representative of uninfluenced (30 °C) and clearly influenced cases (110 °C), as discussed below. The absence of abrupt variation of load in the post-peak region observed in all load-displacement curves reveals stable crack propagation. Two branches constitute the corresponding Resistancecurves obtained in fracture tests (Fig. 5(b)). The initial rising trend reflecting the formation of the fracture process zone is followed by a steady-state plateau defining the fracture energy under selfsimilar crack growth. In the case of 30 °C, for example, the plateau values were found within the range of 0.15–0.38 (N/mm), pointing to an average value of 0.26 N/mm, which is an indication of consistent results, owing to the fact that wood is a natural material with important scatter in its mechanical properties. For 110 °C the attained range was 0.16–0.28 (N/mm) with a mean value of 0.19 N/mm, revealing a decrease of 27% relative to the 30 °C case. In the range of 30°–90 °C no noticeable change of the fracture energy (plateau value) has been observed.

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matrix substances [17]. In addition, the higher the temperature, the more free water existing in wood evaporates, which contributes to the embrittlement of the cell walls, visibly noticed in Fig. 7(b). The numerical model was employed to replicate the loaddisplacement curves using the critical energy release rate (GIc ) obtained experimentally, considering GIc ¼ GIl þ GIb (Fig. 4). The remaining cohesive parameters (i.e., ru , db , rb ) were identified through an inverse method aiming to replicate numerically the experimental load-displacement curve. Fig. 8 shows an example of the agreement obtained following this procedure, for 40 °C. The evolution of the cohesive parameters of the CL (Fig. 4) as a function of the exposure temperature is plotted in Fig. 9. The ultimate values of stress (ru ) and relative displacement (du ) decrease for T > 90 C as a result of the decrease on the fracture energy. This effect is also visible on the stress relative to the inflection point (rb ), although the corresponding relative displacement (db ) does

Fig. 5. Load-displacement curves and corresponding R-curves of the DCB at (a) 30 °C and (b) 110 °C.

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The global set of results shows that the initial specimen stiffness k, (i.e., the inverse of initial compliance C 0 ), is not visibly affected by the temperature in the examined range (Fig. 6(a)). Regarding the ultimate load (P u ), one can observe that Pinus pinaster Ait. is not noticeably influenced in the range of temperatures within 30°–90 °C (Fig. 6(b)), although a visible difference is perceived for temperatures higher than 90 °C. A similar tendency is observed on the value of the critical energy release rate (GIc ) (Fig. 6(c)). This material degradation is an indication that some constituents of wood are being affected over 90 °C. In fact, comparing Fig. 7(a) and (b), it is perceived a more irregular surface texture at 110 °C, revealing a higher degradation of wood micro-structure due to temperature action. Since wood is constituted by cellulose (40%–50%), hemicellulose (15%–25%) and lignin (15%–40%) [17], a plausible reason for the noticed modification in the fracture surface that reflects on the ultimate load and fracture toughness is associated to the material transformation that is undergone by those natural polymers within the range of tested temperatures. In effect, the most relevant transformation that occurs in wood under temperature exposure is known as glass transition temperature (T g ), which allows internal tension relieves by the molecular and microstructural re-organization of wood [18]. The glass transition temperatures of the chemical components of wood differ considerably. Hence, T g of cellulose and hemicellulose are in the range of 150–250 °C [5], being within the range of 60–90 °C for wood lignin [19]. Although these values depend on the wood species and moisture content, they are a clear indication that the observed reduction of mechanical properties is influenced by softening of the lignin component. This behaviour is due to the fact that lignin is the encrusting substance solidifying the cell wall associated with

Ultimate load Pu (N)

70 60 50

40 30 20 10 0 30

40

50

60 70 80 Temperature, T (ºC)

90

100

110

Fig. 6. Resume of results obtained in the experimental tests in the range of tested temperatures: (a) Initial stiffness, (b) Ultimate load, and (c) Critical energy release rate.

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Fig. 7. SEM analyses of wood fractured surfaces at (a) 30° and (b) 110 °C (different scales). N: Notched region; P-C: Pre-Cracked region; F: Fractured region.

σu (MPa) su

σ δbb (mm)

σb (MPa) fb

σu (mm) δc

1.6

Stresses, s (MPa)

2.0

1.2

1.5 0.8 1.0 0.4

0.5 0.0

0.0

20 Fig. 8. Numerical agreement obtained with the cohesive zone model for the DCB test at 40 °C.

Displacements, δ (mm)

2.5

30

40

50

60

70

80

90 100 110 120

Temperature, T (ºC) Fig. 9. Evolution of the parameters of the bilinear cohesive law for the DCB test in the range of temperatures from 30° to 110 °C.

not reveal any evident trend in the range of analysed temperatures. It can be concluded that the reduction of fracture energy for T > 90 C reflects mainly on its fibre-bridging component (i.e., GIb in Fig. 4). A plausible reason for this behaviour can be attributed to the migration of water in the wood walls that occurs around 100 °C. This causes the reduction of the glass transition temperature (T g ) of wood polymeric components [20], promoting the

weakening of the fibre-matrix interface [21], and consequently reducing the fibre-bridging energy component. This aspect is also visible in Fig. 10, which represents the cohesive laws obtained for the two extreme temperatures of the range considered. Additionally, since the area circumscribed to CL represents the fracture energy, then it can be settled that the reduction of fracture energy

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tures. In addition to this aspect, it is also highly relevant to consider the influence of temperature on the viscoelastic behaviour of Pinus pinaster Ait., which will be analysed by the authors in the coming works.

Declaration of Competing Interest None. Acknowledgements

Fig. 10. Cohesive laws of the DCB test obtained for 30° and 110 °C.

between 30 and 100 °C is evident (Fig. 10), which means that reduction factors should be considered in the fracture properties when wood is exposed for a long time to high temperatures in the context of timber construction.

The first author acknowledges FCT for the conceded financial support through the reference project UID/EEA/04436/2019. The second author acknowledges the ‘‘Laboratório Associado de Energia, Transportes e Aeronáutica” (LAETA) for the financial support by the project UID/EMS/50022/2013, and to the funding of Project NORTE-01-0145-FEDER-000022 – SciTech – Science and Technology for Competitive and Sustainable Industries, co-financed by Programa Operacional Regional do Norte (NORTE2020), through Fundo Europeu de Desenvolvimento Regional (FEDER).

5. Conclusions References The influence of temperature on mode I fracture behaviour of wood Pinus pinaster Ait. in the RL fracture system was studied in this work. The double cantilever beam (DCB) test was employed to get the Resistance-curves of specimens previously exposed, during 12 h, to a temperature in the range of 30–110 °C. An equivalent crack length based procedure was used to get those curves using exclusively data ensuing from load-displacement curves registered in the course of the experimental tests. This aspect is relevant owing to difficulties on crack length monitoring inside the climate chamber. A cohesive zone analysis considering a trilinear law was performed in order to assess the influence of the temperature on the cohesive parameters defining the softening law. Considering the objectives stated in Section 1.1, the following conclusions were drawn: 1. The initial specimen stiffness is not noticeably affected by the temperature in the examined range of temperatures. The ultimate load is not visibly influenced in the 30°–90 °C temperature range, although an evident difference is perceived for temperatures higher than 90 °C. 2. It was observed that fracture energy diminishes for exposures to temperatures superior to 90 °C. This was attributed to degradation of lignin whose glass transition temperature is close to this value and of evaporation of free water, which contributes to material embrittlement. The cohesive laws representative of the wood fracture behaviour were determined by an inverse method. 3. The obtained cohesive parameters reveal that ultimate and inflection point stresses diminish for temperatures higher than 90 °C, although the relative displacement corresponding to the inflection point does not vary noticeably. It was concluded that the embrittlement process occurring over 90 °C reflects mostly on the fibre-bridging fracture process. 4. As a general statement, it can be affirmed that Pinus pinaster Ait. suffers degradation of its fracture properties over 90 °C, mainly due to thermal deterioration of lignin and evaporation of free water. This perception must be taken into account in the design of structures eventually submitted to these conditions. An appropriate reduction factor of its properties measured at ambient temperature must be considered, when it is expectable that structures are submitted to long exposures to high tempera-

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