Failure mechanism of softwood under low-cycle fatigue load in compression parallel to grain

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Failure mechanism of softwood under low-cycle fatigue load in compression parallel to grain

Gong, Meng1 and Smith, Ian2

ABSTRACT

Low-cycle fatigue of small clear specimens (6 by 6 by 24 mm) of air-dry black spruce (Picea mariana) under parallel-to-grain compression was investigated. Load control was used with a peak stress level of 90 percent of the static compressive strength, and a load frequency of 0.5 Hz. Duty ratios of 0.05, 0.50 and 0.95 were adopted for square waveforms. Matched ‘pure’ creep tests were carried out and the deformation compared with accumulated deformation under cyclic load. Damage was quantified in terms of the permanent microstructural changes (kinks) in the tracheid walls. It was found that the deformation of creep specimens is larger than that of fatigue specimens, but the relative creep is lower than the relative cyclic creep. The accumulated time to failure (lifetime) of fatigue specimens increases with any decrease in the duty ratio. Creep specimens have the longest lifetime. ‘Cyclic effect’ plays a predominant role in the damage accumulation in fatigue specimens. The damage accumulation due to creep and fatigue differs. In creep tests, damage mainly develops from the existing kinks, which are formed during the initial loading. In fatigue tests, it develops from both existing kinks, which are formed during the first load cycle, and newly formed kinks due to the load cycling. The number of kinks exhibits a strong relationship with the relative cyclic creep and relative creep, and is a good ‘direct’ damage indicator.

INTRODUCTION

Structural wood systems fail during extreme events, such as hurricanes and earthquakes, which cause high-stress-level cyclic load conditions in members. Although an extreme event may not last very long, damage accumulation is still a time-dependent process because wood is a visco-elastic material. The damage process is termed low-cycle fatigue (LCF). Thus, LCF failures result from relatively few load cycles at a high stress level. Gong and Smith (1999a) found that the accumulated compressive strain in softwood fatigue specimens is smaller than that in creep specimens, but the ‘relative cyclic creep’ is larger than ‘relative creep’ if a peak stress level such as 85 percent of static compressive strength (Cmax) is

used. Bonfield et al. (1994) reported that flexural fatigue specimens of chipboard always fail before creep specimens for peak stresses ranging from 50 to 80 percent of static bending strength. They also found that accumulated strain is smaller in fatigue specimens than in creep specimens. These findings suggest that the mechanisms of damage accumulation are different under fatigue and creep loads.

Knowledge of the parallel-to-grain compressive behaviour of wood is important in the design of columns, beams and connections. Compression damage of softwood in the parallel-to-grain direction can first be detected in the form of ‘kinks’ in the cell walls (Robinson 1920; Kollmann 1963; Scurfield et al. 1972; Dinwoodie 1989; Hoffmeyer 1993). A kink is a permanent microstructural change in a cell wall, and results from the reorientation of microfibrils in the middle layer of the secondary cell wall (Hoffmeyer 1993). How kinks initiate and develop is important for understanding the failure mechanism of softwood subjected to either cyclic or sustained loads.

This paper discusses the failure mechanism of softwood under low-cycle fatigue load in compression parallel to grain. Special attention is given to the initiation and development of kinks in cell walls, and to the comparison of failure mechanisms between fatigue and creep specimens. The significance of the findings is explained in the context of engineering design in wood.

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1Graduate Research Assistant 2Professor of Timber Engineering

Faculty of Forestry and Environmental Management

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METHOD

Material and specimen sampling

Air-dry black spruce (Picea mariana) was selected as the research material because of the simplicity and uniformity of its growth structure. The seasoned lumber with an equilibrium moisture content of 14.5 percent was cut to produce 60-mm-long sticks of 6 by 6 mm in cross-section. Sides of sticks were aligned parallel to the radial and tangential planes (American Society for Testing and Materials 1997). Twelve sets of sticks with five replicates each were created following a ‘density-matched’ sampling strategy (Gong and Smith 1999a). These sets were classified into three groups. The first group designated as for ‘lifetime’ tests were used to estimate the accumulated time (lifetime) of specimens under fatigue and creep conditions. The second and third groups were used to evaluate the accumulation of kinks in creep and fatigue tests, respectively. Each stick was cross cut to create two ‘end-to-end’ matched compression specimens (each 24-mm-long). One matched specimen was used to determine static strength and the other in either a fatigue or creep test. Thus, there were 120 tests in total, of which 60 were static tests for reference strengths.

The dimension of small clear prismatic specimens (6 by 6 by 24 mm) was decreased proportionally in terms of the dimension stipulated by American Society for Testing and Materials (1997). There are two main reasons why small specimens were used. First, it is usually difficult to locate a typical failure area from a large specimen that is compressed parallel to grain. Second, it is impossible to directly mount a large specimen onto a microtome. Also, some artificial defects will possibly be created during the manufacture of small specimens from a large specimen. It may be debated whether a small specimen behaves in the same way as a large standard specimen recommended by American Society for

Testing and Materials (1997). According to the observation by C^tJ and Hanna (1982), and the authors, a small specimen

subjected to compressive loading parallel to grain exhibits good similarity to a large specimen in terms of mechanical behaviour and failure mode.

Experimental apparatus and procedure

A servo-hydraulic actuator was employed to perform static, fatigue and creep tests and was calibrated from 0 to 5 kN. Static tests were conducted using the position-control function and a speed of 0.1 mm/min. The load-control function was adopted in fatigue and creep tests. The frequency for data logging was 5 Hz in static and creep tests, and 250 Hz in fatigue tests. A commercial data acquisition system was used to collect three synchronised streams of data (load, cross-head movement and total elapsed time). A specimen was placed concentrically between the loading head and the supporting platen of the testing machine.

Square waveform, a peak fatigue stress of 90 percent Cmax, a stress ratio (R) of 9.0, and a load frequency of 0.5 Hz were

used in fatigue tests, Figure 1. The initial loading rate for creep tests was set at 200 kN/min and the constant creep stress was the same as that in fatigue tests (i.e. 90 percent Cmax). The constant creep stress was attained in about 0.4 seconds.

For the first group, ‘lifetime’ tests contained three types of fatigue tests using square waveform with duty ratios (τ) = 0.05,

0.50 and 0.95, and one pure creep test. The accumulated time and/or number of cycles to failure were recorded. For the second group, ‘creep’ tests had duration of 10, 20, 80 and 320 seconds. For the third group, ‘fatigue’ tests only employed

square waveform with τ = 0.50, and terminated at 5, 10, 40 and 160 load cycles, which correspond to the elapsed time in

creep tests.

To avoid failure at the ends of a specimen, the moisture content in the ends was slightly reduced using special measures (Gong and Smith 1999a). There was a moisture content difference of about 0.5 percent between the central part and the ends.

Preliminary data analysis

Compressive stress and strain are actually negative values by normal convention, but to facilitate plotting, all stress and strain in this paper are treated as positive values. The accumulated deformation in creep tests can be described using the

relative creep (RC) (Bodig and Jayne 1982), which is defined as RC=(DtD0)/D0, where: D0= initial deformation

(mm); Dt = deformation (mm) at time t. Similarly, the accumulated peak deformation in fatigue tests can be described

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(mm) during the first load cycle, CDN= maximum deformation (mm) during the Nth load cycle. To reasonably compare

the data from creep and fatigue tests, D0 is defined as the deformation at time of one second. Thus,D0occurs at the same

time as CD1 because the load frequency is 0.5 Hz in fatigue tests.

Figure 1. Stress ratio (R) and duty ratio (J), where:

Fmin = 0.9 Cmax and Fmax = 0.1 Cmax

Figure 2. Deformation and cyclic deformation in a creep and a fatigue test (J=0.50) Microscopy

To reliably predict wood strength, it is important to have an understanding of the failure mechanism that is based on physical observation (Qin et al. 1999). As early as 1920, microscopy was used to investigate the relationship between the minute structure and mechanical properties of wood (Robinson 1920). Many efforts were made since then to study the morphology of failure surfaces using optical microscopy, scanning electron microscopy (SEM) and transmission electron microscopy. In this study, two types of microscopy were employed. First, all specimens were observed under a ‘dark-field incident’ light microscope to examine the failure surface. Second, at least three specimens in each set were selected for microtoming. Each specimen was soaked and cut to produce three or four sections. The authors adopted parameters for

manufacturing the sections based on the microtoming techniques developed by Dinwoodie (1966) and Keith and C^tJ

(1968). Sections were cut parallel to the radial plane, the cutting angle was 10 degrees, the drawing angle was kept as small

as possible, the section thickness was 10 :m, and the microtome knife edge was parallel to the grain of the wood. The

sections were examined under a polarised-light microscope to detect kinks in cell walls and any changes in cell shape.

RESULTS AND DISCUSSION

Relative creep and relative cyclic creep

Due to its visco-elastic property, wood exhibits a time-dependent deformation (creep) when it is subjected to a sustained or cyclic load. The term creep in fatigue tests is used to describe the change of deformation that occurs during cyclic loading at a fixed load level. The magnitude of creep in fatigue tests is related to the peak load, load frequency, waveform, stress-ratio, and the number of load cycles (Kellogg 1960; Bach 1975; Bordonne et al. 1987; Clorius et al. 1996; Gong and Smith 1999a, 1999b). During low-frequency cyclic load tests, creep is reported to dominate the damage accumulation (Clorius et al. 1996). The severity of the creep effect has been found to depend on the peak stress using a load frequency of 0.2 Hz and a triangular waveform (Gong and Smith 1999a). Damage is accumulated most rapidly under square waveforms with a high duty ratio (Gong and Smith 1999b).

Progressive accumulation of deformation occurred during creep and fatigue tests, Figure 2. All the accumulated deformation in creep tests is larger than that in fatigue tests, Figure 3. This agrees with the findings by Bonfield et al. (1994), and Gong and Smith (1999a). Although the peak fatigue stress is equal to the constant creep stress (i.e. 90 percent

Cmax), the accumulated strain (deformation) in fatigue tests was reported to be dependent on the mean stress (Bonfield et al.

1994). This mean stress, which is equal to 50 percent Cmax and only 56 percent of constant creep stress, might cause the

0 2 4 6 8 10 12 14 16 18 20 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Creep Fatigue Deformation (mm) Time (sec) Stress Time Fmin Fmax T Td R = Fmin/Fmax J= Td/ T

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lower accumulated deformation. The relative cyclic creep (RCC) and relative creep (RC) having a duration of 320 seconds are plotted in Figure 4, in which each curve represents an average for a set of five specimens. RCC is clearly larger than

RC suggesting that deformation accumulation rate is larger in fatigue tests than in creep tests. This in turn implies that

damage accumulates more rapidly in fatigue tests than in creep tests in the same loading period. The same results were obtained from the other three sets with a duration of 10, 20, and 80 seconds, respectively. Bonfiled et al. (1994) found that fatigue specimens always fail first, although they showed less deformation than creep specimens until just before failure. They studied fatigue and creep behaviour of structural grade chipboard subjected to flexure and indicated that other processes may occur concurrently with creep in chipboard. The ‘cyclic effect’ may be one of the causes. Based on accumulated deformations and deformation accumulation rates, it appears reasonable to suppose that the failure mechanisms differ between creep and fatigue load conditions.

Figure 3. Average accumulated deformations under creep and fatigue tests

Figure 4. Average relative creep and relative cyclic creep

Cyclic effect on fatigue behaviour under square waveform loading

Fatigue is a process of damage accumulation under cyclic loading. By hypothesising that there is no interaction between creep and fatigue mechanisms, Kohara and Okuyama (1992) developed a linear damage accumulation model to illustrate fatigue behaviour of spruce specimens subjected to repeated loading in flexure tests at load frequencies of 1.0 and 0.1 Hz,

i.e. + =1.0

fatigue

creep N

N T

T , where: T is the total loading time to failure, N is the total number of load cycles to failure, T

creep is

the pure creep lifetime, and Nfatigue is the pure fatigue life. creep T

T reflects the effect of load duration (creep) and

fatigue N

N the

effect of cyclic loading (fatigue). Having found that their data did not fit this linear model well, they modified the model to

a non-linear format, i.e. ( ) +( )b =1.0

fatigue a

creep N

N T

T , where: a and b are model constants.

Table 1. Average loading time and cycle number to failure

Duty Ratio Lifetime (sec) T (sec) N (cycle) T/Tcreep N/Nfatigue SUM PN (%)

1.00 33151 33151 0 1 0 1 0

0.95 1339 1272 670 0.03838 0.16174 0.20012 80.8

0.50 7055 3528 3528 0.10641 0.85199 0.95840 88.9

0.05 8281 414 4140 0.01249 1 1.01249 98.8

Note: SUM means the sum of T/Tcreep and N/Nfatigue; PN the percentage of N/Nfatigue to SUM.

Table 1 summaries the ‘lifetime’ tests. The fatigue test with J=0.05 is assumed to be a pure fatigue test, while J=1.0

corresponds to a pure creep test. The effect of creep on the number of cycles to failure is obvious, i.e. the accumulated time

to failure (lifetime) decreases with an increase of duty ratio (J). Creep specimens have the longest lifetime. PN in Table 1

reflects the contribution of ‘cyclic effect’ to the damage accumulation. With decreasing J from 0.95 to 0.05, the

0 40 80 120 160 200 240 280 320 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Creep Fatigue 160 140 120 60 80 100 40 20 0 Number of cycles Deformation (mm) Time (sec) 0 40 80 120 160 200 240 280 320 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350 20 40 60 80 100 120 140 160 Number of cycles Relative creep Relative cyclic creep

Relative creep / relative cyclic creep

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contribution percentage by the number of cyclic loading increases by about 20 percent, suggesting the effect of load duration becomes less marked. The ‘cyclic effect’ is predominant in fatigue. By substituting a = 1.0 and b = 0.02 (Kohara and Okuyama 1992) into the modified model, the sum of contributions from creep and fatigue is around 1.0, Table 2, indicating that the current data supports the non-linear model by Kohara and Okuyama (1992). The high PN value (i.e. larger than 90 percent) further emphasises the contribution of ‘cyclic effect’ in the damage accumulation in fatigue tests, suggesting that damage accumulated rate is higher in fatigue specimens. This might be the reason why relative cyclic creep is always larger than relative creep. Therefore, any models used for predicting creep behaviour should not be extrapolated to predict fatigue behaviour.

Table 2. Verification of non-linear model using a=1.0 and b=0.02

Duty Ratio (T/Tcreep)1.0 (N/Nfatigue)0.02 SUM PN (%)

1.00 1 0 1 0

0.95 0.03838 0.96422 1.00260 96.2

0.50 0.10641 0.99680 1.10321 90.4

0.05 0.01249 1 1.01249 98.8

Morphology of wood failure using polarised-light microscopy

Figure 5. Kinks (arrows) at various loading times in creep tests (200×)

Surfaces of all specimens were examined by means of a ‘dark-field incident’ light microscope. At least three specimens in a set were selected and microtomed to produce sections for observing kinks under a polarised-light microscope. Figure 5 illustrates the formation and development of kinks in creep tests. Arrows on the figures indicate representative locations of

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kinks. It was found that kinks have a relatively uniform distribution across tracheids in the radial-longitudinal plane in the creep specimens. Most kinks exist in the latewood tracheids (Keith 1971). The number of kinks does not change significantly over time, Table 3.

Table 3. Number of kinks at various loading stages of fatigue and creep tests Number of load cycle / Duration (seconds)

Test type

5 / 10 10 / 20 40 / 80 160 / 320

Fatigue (J=0.5) 6 48 82 108

Creep 32 24 40 42

Note: The number of kinks is an average of three sections from three specimens.

Figure 6 shows the formation and development of kinks in fatigue tests. It was discovered that kinks are generated first among the latewood tracheids close to the boundary between two growth rings, and then develop from latewood to earlywood tracheids resulting in the buckling of earlywood tracheids. This is not surprising since the stiffness of the neighbouring cell walls between latewood and earlywood tracheids is less than that of the combination of two latewood tracheids. The stiffest tracheid wall combination sustains the most stress and therefore is damaged first. Kinks accumulate quickly as the number of load cycles is increased, and many new kinks are initiated, Table 3.

Figure 6. Kinks (arrows) at various load cycles in fatigue tests with a duty ratio of 0.5 (200×)

Figures 5 and 6 reveal that the failure mechanisms of wood are different for creep and fatigue tests. Damage accumulation in creep tests is predominantly the growth of a limited number of kinks formed in the initial stage of loading sequence. This is in favour of the explanation to mechano-sorptive creep mechanism by Hoffmeyer and Davidson (1989). By

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contrast, damage accumulation beyond the first load cycle in fatigue tests results both from existing kinks and new ones. Although not studied explicitly, it seems clear that the stress ratio (R) will control the rate at which new kinks form during load cycling. These observations explain why the lifetime of a fatigue specimen is much shorter than that of a creep specimen, Table 1, and why the relative cyclic creep is larger than relative creep, Figure 4. The peak stress plays an important role in determining lifetime of a specimen subjected to either a sustained or cyclic load. Gong and Smith (1999a)

found that most specimens failed in creep tests with a peak stress of 95 percent Cmax in a relative short time (about 10

minutes) but no specimens failed in fatigue tests with the same peak stress in the same duration. This suggests that

conclusions here should not be extrapolated to cases where the peak stress is more than 90 percent Cmax.

In summary, failure process of wood under sustained loads can briefly be divided into three separate stages: 1) kink initiation, 2) kink growth, and 3) macroscopic failure. However, failure process is a little complicated under cyclic loads. With the initiation and growth of kinks, some new kinks will join the existing kinks due to ‘cyclic effect’, resulting in an accelerated failure process.

By plotting the number of kinks versus time in Figure 7, it is found that there exists a similarity between Figure 4 and Figure 7. Both RCC/RC and the number of kinks increase in a non-linear way over time. It may be reasonable to infer that accumulated deformations in both fatigue and creep tests are the result of kink accumulation. The relationships between the number of kinks and accumulated deformations are shown in Figure 8, which supports the findings by Hoffmeyer (1993), i.e. RCC/RC increases with increasing the number of kinks. The number of kinks is a good ‘direct’ damage indicator in specimens subjected to compressive stress parallel to grain. However, detailed quantitative analysis on this point needs further investigation.

Figure 7. Average number of kinks Figure 8. Average number of kinks vs. relative cyclic

creep / relative creep

CONCLUSION

The nature of failure in softwood can be accredited to the formation of kinks in the latewood tracheid walls in parallel-to-grain compression regardless of whether the load is applied in a creep or fatigue test. The number of kinks exhibits a strong relationship with the relative cyclic creep and relative creep, and is a good ‘direct’ damage indicator. The damage accumulation due to creep and fatigue differs. The damage loci in creep specimens are mainly kinks formed during the initial loading. For fatigue specimens, new kinks are initiated due to cyclic loading. This is the reason why relative creep, as observed in pure creep experiments, is smaller than the relative cyclic creep. The practical implication of this is that high-stress-level creep or creep rupture tests employing constant loading should not be extrapolated to predict behaviour under cyclic load sequences.

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 0 20 40 60 80 100 120 Creep Fatigue Number of kinks Time (sec) 0 20 40 60 80 100 120 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Relative creep Relative cyclic creep

Relative cyclic creep / relative creep

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ACKNOWLEDGEMENTS

This paper relates to work under the Research Grant ‘Control of failure mechanisms for structural timber members and connections’ held by the second author and funded by the Natural Sciences and Engineering Research Council of Canada. Special thanks are due to Dr. Y.H. Chui for his helpful comments on the previous draft of this paper.

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