In this article, dynamic method and static method of testing Poisson’s ratio of OSB (Oriented Strand Board) were proposed. Through modal and static numerical analyses, the position where the transverse stress is equal to zero was determined. The binary linear regression method was applied to express the gluing position of the strain gauge as a relational expression that depended on the length-width ratio and width-thickness ratio of the cantilever plate. Then the longitudinal and transverse Poisson’s ratios of OSB were measured by the given dynamic and static methods. In addition, the test results of OSB Poisson’s ratio were analyzed with the probability distribution of random variables. The results showed that using the proposed dynamic method and static method, the test results for longitudinal and transverse Poisson’s ratios of OSB were quite consistent, despite the gluing position of the strain gauges being different. And these OSB Poisson’s ratios were accorded with that obtained by the axial tensile method and the four-point bending method. OSB longitudinal and transverse Poisson’s ratios followed Weibull distribution.

OSB is currently recognized as a three-layer structure board with mature technology, fast development, and application prospects. Since it came out in the late 1970s, it has been widely used in many fields such as construction, packaging, furniture, and decoration because of its good stability, low material consumption, high strength, and environmental protection. The production process of OSB can be described as follows. Firstly, wood is sawed along the grain direction to obtain flat, narrow and long chips with certain size (generally 40–100 mm in length, 5–20 mm in width, 0.3–0.7 mm in thickness). Then adhesives and additives were applied to these dried and screened wood chips. And finally these chips were oriented and hot pressed to form a three-layer structure board [

In the outer layer and core layer of OSB, the texture direction of the wood chips is usually parallel and perpendicular to the longitudinal axis of the board. From the observation of the board surface, it can be found that the shape and size of the chips are irregular, and the laying direction of some chips deviates from the longitudinal direction of the board, which means there is a certain randomness in the shape, size and laying direction of the chips in the outer layer. In addition, sometimes there are even small holes or blisters in the board. The above factors have led to the non-uniformity of OSB.

Elastic modulus, shear modulus and Poisson’s ratio are the basic parameters to characterize the mechanical properties of materials, which need to be tested [

Fan et al. [_{L}, _{R}, _{T}, _{LR}, _{LT}, _{RL}, _{RT}, _{TL}, _{TR} (

The purpose of this study is to explore the applicability of dynamic and static methods for testing OSB longitudinal and transverse Poisson’s ratios. Based on the previous researches [

The ANSYS 12.1 modal and static bending program blocks were used to analyze the static and dynamic stress and strain of the cantilever plate specimens. The ANSYS calculation used Solid 45 units and 50 × 10 network division. The input material constants are shown in

Material | Density (kg/m^{3}) |
Direction | _{x} (GPa) |
_{y} (GPa) |
_{z} (GPa) |
_{xy} |
_{yz} |
_{xz} |
_{xy} (GPa) |
_{yz} (GPa) |
_{xz} (GPa) |
---|---|---|---|---|---|---|---|---|---|---|---|

OSB | 650 | Longitudinal | 6.34 | 2.41 | 2.41 | 0.34 | 0.13 | 0.13 | 1.20 | 0.4 | 0.4 |

Transverse | 2.41 | 6.34 | 2.41 | 0.13 | 0.34 | 0.13 | 1.20 | 0.4 | 0.4 |

Note:

The stress and strain calculation of OSB cantilever plate first-order bending mode adopted ANSYS modal program blocks. And that of OSB cantilever plate static bending adopted ANSYS static bending program blocks. For the static method, load was a concentrated force acting on the middle of the free end of the cantilever plate; its value was 10 N, and the direction was perpendicular to the plate surface downward.

_{x}, _{y}, _{x}, and _{y} were the output parameters of ANSYS calculation.

The stress and strain calculation results of OSB cantilever plate first-order bending mode and static bending showed: during the first-order bending and the static bending vibration of OSB cantilever plate, there were points where the transverse stress was equal to 0. Although the positions of the points were different, the absolute value of the ratio of the transverse strain to the longitudinal strain was equal to the value of Poisson’s ratio inputted in ANSYS (

_{y} = 0 on the midline. This position varied with the length-width ratio and width-thickness ratio of the cantilever plates, as well as dynamic test or static test. The value of −_{y}_{x} at position _{y} = 0 was equal to the Poisson’s ratio value inputted in ANSYS calculation.

Specimen | Size (mm × mm × mm) | Density (kg/m^{3}) |
Moisture content (%) | Clamping depth (mm) | Outer cantilever extension (mm) | Length-width ratio | Width-thickness ratio |
---|---|---|---|---|---|---|---|

L-A | 454× 74 × 9.75 | 650 | 9 | 120 | 334 | 4.5 | 7.6 |

T-A | 454× 74 × 9.75 | 650 | 8 | 120 | 334 | 4.5 | 7.6 |

L-B | 435× 70× 9.75 | 650 | 9 | 120 | 315 | 4.5 | 7.2 |

In _{y}/_{x}_d represents the absolute value of the ratio of the transverse dynamic strain to the longitudinal dynamic strain of the point on the midline, which changing along the longitudinal direction _{y}/_{x}_d represents the value of the ratio of the transverse dynamic stress to the longitudinal dynamic stress of the point on the midline during the first-order bending vibration; OSB0°_−_{y}/_{x}_s represents the absolute value of the ratio of the transverse static strain to the longitudinal static strain of the point on the midline during the static bending; OSB0°__{y}/_{x}_s represents the value of the ratio of the transverse static stress to the longitudinal static stress of the point on the midline during the static bending.

For the transverse specimens in

The material Poisson’s ratio is defined as the absolute value of the ratio of the transverse strain to the longitudinal strain of the specimen under axial tension. In the axial tension state, the specimen is subjected to a unidirectional stress state, which means only the longitudinal stress _{x} exist in the specimen, and the transverse stress _{y} = 0. Since the cantilever plate has a position of _{y} = 0 in both condition of static bending and first-order bending vibration, if the transverse and longitudinal strain gauges are glued at this position, the absolute value of the ratio of the transverse strain to the longitudinal strain obtained by the test can be regarded as Poisson’s ratio. Its effectiveness needs to be verified by other test methods, such as the axial tension method or the four-point bending method.

The positions where the transverse stress is equal to 0 in dynamic and static conditions had been calculated from totally 48 calculation schemes, using OSB longitudinal and transverse cantilever plates with length-width ratio

The gluing position of strain gauges for dynamic test of OSB Poisson’s ratio was:

Longitudinal:

Transverse:

The gluing position of strain gauges for static test of OSB Poisson’s ratio was:

Longitudinal:

Transverse:

In

Dynamic test: the definition of Poisson’s ratio in the frequency domain is the ratio of the linear spectral amplitude of the transverse strain to that of the longitudinal strain at the first-order bending frequency on the cantilever plate spectrum diagram, which is:

Static test: the definition of Poisson’s ratio is the absolute value of the ratio of the transverse strain increment to the longitudinal strain increment during the static bending of the cantilever plate, which is:

The direction of the length of OSB for the test is longitudinal (0°), which is taken as the x-axis. The direction of the width is transverse (90°), which is taken as the y-axis. And the direction of the thickness is taken as the z-axis. The positive x, y, and z axes follow the right-hand spiral rule.

OSB (made in China) was purchased from Tianshen New Material Co., Ltd., China. The strands were made of pine (

Test instruments and accessories: CRAS vibration and dynamic signal acquisition and analysis system, including signal conditioning instrument, AZ acquisition box and supporting analysis software; YD-28A dynamic strain indicator; cantilever plate holding device; tensile test device; four-point bending test device; BX120-10AA strain gauges (sensitivity coefficient 2.08%, strain grid 10 mm × 5 mm); bridge boxes; force hammer; glue; several weights; several wires.

After the surface of the board was smoothed with wood sandpaper, the strain gauges would be glued on the position as specified in

For OSB longitudinal specimen L-A (334 mm × 74 mm × 9.75 mm), according to

Considering the randomness of the size and laying direction of the OSB wood chips, the specimen was sawed 34 mm from its free end after the dynamic test of the longitudinal Poisson’s ratio to illustrate the correctness of

When applying this processing method to dynamic and static tests of Poisson’s ratio, the state of the wood chips where the strain gauges were glued did not change. But the position of the strain gauges on the cantilever plate of the same span (334 mm) had changed. This change was determined by the

For OSB transverse specimen T-A (334 mm × 74 mm × 9.75 mm), according to

Similar to

In

In this chapter, for OSB longitudinal specimen L-B (315 mm × 70 mm × 9.75 mm), the gluing position was calculated according to

The test process is shown in

When performing the dynamic test of OSB Poisson’s ratio (

When performing the static test of OSB Poisson’s ratio (

The method of loading weights was used to perform the static test, and each specimen was tested three times with using two-level loading increment. The mean value of −∆_{y}/∆_{x} calculated from the last two tests was taken as the test result of OSB Poisson’s ratio. As shown in

The longitudinal specimens L-A for dynamic test were sawed into tensile specimens (360 mm × 36 mm × 9.75 mm), and the longitudinal and transverse strain gauges were located at the midpoint of the midline. In order to avoid bending strain caused by the misalignment of the clamped specimen, the longitudinal and transverse strain gauges on the upper and lower surfaces of the specimen are connected in series, respectively. Then the strain gauges were connected to two bridge boxes according to the 1/4-bridge wiring method.

The initial load was 0.8 kN, and the end load was 1.8 kN. The transverse and longitudinal strain increments within the load range were used to calculate the Poisson’s ratio. Each specimen was subjected to axial tensile tests three times. The last two test data was taken to calculate the Poisson’s ratio, and the calculation equation is same as

The transverse specimens T-A were sawed into four-point bending specimens (280 mm × 28 mm × 9.75 mm). The longitudinal and transverse strain gauges on the upper and lower surfaces were located in the middle of the specimens. Then the half-bridge wiring method was adopted to measure the transverse and longitudinal strain increments (using loading weights, with loading increment 2.0825 N), and OSB transverse Poisson’s ratio was obtained. Each specimen was subjected to four-point bending test three times, and Poisson’s ratio was also calculated from the last two test data according to

The frequency spectrums obtained in dynamic test of OSB longitudinal specimen T-A-4 are shown in

The first-order bending frequency of the cantilever plate of T-A-4 was 41.88 Hz; the transverse strain linear spectral amplitude was 1.39

The peak value of the longitudinal strain waveform and that of the transverse strain waveform at the fundamental frequency of T-A-4 were in opposite sign. Poisson ratio calculated at 82.42 ms was _{y}/_{x} = 0.341, while that was 0.357 at 201.95 ms. OSB longitudinal Poisson’s ratio measured in the time domain (0.341, 0.357) was quite consistent with that measured in the frequency domain (0.348).

For Specimens L-A and T-A, OSB longitudinal and transverse elastic modulus and in-plane shear modulus were tested using the free plate torsional mode method proposed in article [^{nd} and 3^{rd} columns of ^{th}, 5^{th}, 6^{th}, and 7^{th} columns of

Specimen |
Elastic modulus (GPa) | Shear modulus (GPa) | Poisson’s ratio | |||
---|---|---|---|---|---|---|

First-order bending mode method | Static bending method | Axial tensile method | Four-point bending method | |||

Longitudinal | 6.34 (6.9%) | 1.15 (4.5%) | 0.342 (22.6%) | 0.334 (22.9%) | 0.321 (28.8%) | – |

Transverse | 2.41 (9.7%) | 1.20 (7.8%) | 0.131 (32.6%) | 0.126 (30.3%) | – | 0.122 (36.7%) |

Note: The percentage in parentheses is the coefficient of variation.

For specimens T-B (315 mm × 70 mm × 9.75 mm, ^{nd} and 3^{rd} columns of

In order to verify the applicability of ^{th}, 5^{th} 6^{th} and 7^{th} columns of

Number (longitudinal) | Poisson’s ratio | |||||
---|---|---|---|---|---|---|

First-order bending mode method (gluing position 138 mm) | Static bending method (gluing position 170 mm) | First-order bending mode method (gluing position 124 mm) | Static bending method (gluing position 141 mm) | First-order bending mode method (gluing position 114 mm) | Static bending method (gluing position 120 mm) | |

L-B-1 | 0.323 | 0.335 | 0.346 | 0.323 | 0.358 | 0.324 |

L-B-2 | 0.378 | 0.467 | 0.391 | 0.449 | 0.413 | 0.453 |

L-B-3 | 0.314 | 0.330 | 0.333 | 0.325 | 0.346 | 0.348 |

L-B-4 | 0.359 | 0.590 | 0.374 | 0.577 | 0.384 | 0.619 |

L-B-5 | 0.246 | 0.193 | 0.245 | 0.194 | 0.242 | 0.197 |

L-B-6 | 0.362 | 0.320 | 0.373 | 0.314 | 0.388 | 0.311 |

L-B-7 | 0.319 | 0.386 | 0.331 | 0.381 | 0.342 | 0.372 |

L-B-8 | 0.298 | 0.149 | 0.310 | 0.153 | 0.328 | 0.155 |

L-B-9 | 0.328 | 0.277 | 0.321 | 0.268 | 0.326 | 0.271 |

Mean | 0.325 | 0.339 | 0.336 | 0.332 | 0.347 | 0.339 |

Coefficient of variation | 12.1% | 39.5% | 13.0% | 38.7% | 14.2% | 40.7% |

The cantilever plate first-order bending mode method and static bending method were both based on the patch method with the transverse stress of the cantilever plate equal to 0, which was described as

Firstly, according to the size of the cantilever plate,

For cantilever plates with the same length-width ratio and width-thickness ratio, the difference between OSB longitudinal and transverse Poisson’s ratios obtained by the cantilever plate first-order bending mode method and the cantilever plate static bending method, was within 4.1% (

OSB longitudinal Poisson’s ratio obtained by the cantilever plate first-order bending mode method increased slightly (about 6.8%) as the length-width ratio of the specimen decreased, and that obtained by the cantilever plate static bending method basically did not change with the length-width ratio (

OSB Poisson’s ratios obtained by the cantilever plate first-order bending mode method and the cantilever plate static bending method were quite consistent with that obtained by the axial tensile method and the four-point bending method. The relative errors of OSB longitudinal and transverse Poisson’s ratios obtained by two proposed methods and two confirmatory methods were all within 7.4% (

In summary, the patch method with the transverse stress of the cantilever plate equal to 0 (

Refer to

Whether it was analyzed from OSB longitudinal elastic modulus, longitudinal Poisson’s ratio and related shear modulus obtained by the longitudinal cantilever plate test, or from OSB transverse elastic modulus, transverse Poisson’s ratio and related shear modulus obtained by the transverse cantilever plate test, there did not seem to exist a consistent relationship,

For example,

The product quality of OSB mainly depends on wood species, glue composition, orientation of wood chips, relative thickness between layers, and pressure applied during processing. These factors will inevitably affect the performance parameters of OSB.

During the study of the dynamic and static test methods of OSB Poisson’s ratio, it was found that the ratio of the transverse strain _{y} to the longitudinal strain _{x} on the upper and lower plate surfaces at the same longitudinal position of the cantilever plate, had a large difference sometimes. For example, for the longitudinal B specimen No. 2, at a distance of 138 mm from the fixed support edge (the strain guage gluing position for the dynamic test of OSB longitudinal Poisson’s ratio), the test value of _{y}/_{x} on the upper plate surface was 0.269. And the test value of −_{y}/_{x} on the lower surface was 0.497, which was close to twice the value of that on the upper surface.

This non-uniformity of OSB material made it difficult to verify the validity of

In the test, OSB specimens made in China were used first. It was found that the dispersion of OSB Poisson’s ratio test values was related to the size and laying direction of the outer layer wood chips of OSB where the strain gauges were glued. If the strain gauges were glued on large-size wood chips or those whose laying direction deviated from the longitudinal direction of the board, the test value of OSB Poisson’s ratio obtained would be too small or too large, resulting in a greater dispersion of OSB Poisson’s ratio.

To illustrate this phenomenon, 10 longitudinal specimens and 8 transverse specimens were sawed from an entire OSB made in Canada (purchased from Norbord Inc., Canada, with poplar (^{nd}, 3^{rd} and 4^{th} columns of ^{th} column of

Specimen direction | Poisson’s ratio | |||
---|---|---|---|---|

First-order bending mode method | Four-point bending method | |||

Longitudinal | 0.318 (26.0%) | |||

0.308 (23.1%) | 0.314 (23.4%) | 0.319 (25.1%) | ||

Transverse | – | 0.170 (32.0%) | ||

0.173 (25.5%) | 0.174 (25.0%) | – |

Note: The percentage in parentheses is the coefficient of variation.

The longitudinal and transverse Poisson’s ratios obtained by OSB specimens from China and Canada was summarized as shown in

Place of origin | Specimen direction | Poisson’s ratio | ||
---|---|---|---|---|

First-order bending mode method | Static bending method | Confirmatory test | ||

China | Longitudinal | 0.33 (20.5%) | 0.34 (32.3%) | 0.32 (28.8%) (Axial tensile method) |

Transverse | 0.13 (32.6%) | 0.13 (30.3%) | 0.12 (36.7%) (Four-point bending method) | |

Canada | Longitudinal | 0.31 (23.4%) | – | 0.32 (26.0%) (Four-point bending method) |

Transverse | 0.17 (25.5%) | – | 0.17 (32.0%) (Four-point bending method) |

Note: The percentage in parentheses is the coefficient of variation.

OSB longitudinal Poisson’s ratios of specimens L-A (9 pieces) and L-B (9 pieces) were dynamically tested. And the total 18 test data were arranged from small to large to get the order statistics _{i} (

From the phenomenon that the test points basically fell on a straight line, it could be considered that OSB longitudinal Poisson’s ratio test values conformed to the Weibull distribution.

The shape parameter _{0} = 0.3604 was obtained according to the intercept (1.9035) of the straight line and the longitudinal axis. Therefore,

The distribution function of longitudinal Poisson’s ratio:

The probability density function of longitudinal Poisson’s ratio:

For OSB transverse Poisson’s ratios of specimens T-A (8 pieces), a graph (

The shape parameter _{0} = 0.1483 was obtained according to the intercept (1.9253) of the straight line and the longitudinal axis. Therefore:

The distribution function of transverse Poisson’s ratio:

The probability density function of transverse Poisson’s ratio:

To explore the applicability of dynamic and static methods for testing OSB longitudinal and transverse Poisson’s ratios, the following studies were carried out in this paper: Firstly, ANSYS was used to analyze the stress and strain of the OSB cantilever plate specimens with different length-width ratio and width-thickness ratio. Secondly, the position where the transverse stress is equal to zero obtained in above ANSYS calculation was applied as the gluing position of the strain gauge, and it was expressed as a formula that depends on the length-width ratio and the width-thickness ratio of the cantilever plate through binary linear regression. Thirdly, OSB longitudinal and transverse Poisson’s ratios were measured dynamically and statically using the methods proposed. Fourthly, the axial tensile test and the four-point bending test were also performed to verify the effectiveness of the strain gauge gluing position. Fifthly, the probability distribution of Poisson’s ratio test values was expounded. The main conclusions are as follows:

The cantilever plate first-order bending mode method (dynamic method) and the cantilever plate static bending method (static method) for testing OSB longitudinal and transverse Poisson’s ratios had a reliable theoretical basis through simulation analysis.

OSB longitudinal and transverse Poisson’s ratios obtained by the cantilever plate first-order bending mode method and the cantilever plate static bending method were consistent, with the difference less than 4.1%.

OSB longitudinal and transverse Poisson’s ratios obtained by the cantilever plate first-order bending mode method and the cantilever plate static bending method, were quite consistent with those obtained by the axial tensile method and the four-point bending method.

The patch method with the transverse stress of the cantilever plate equal to 0 (

OSB longitudinal and transverse Poisson’s ratios test values followed Weibull distribution, with characteristics: (1) the probability density functions of the longitudinal and transverse Poisson’s ratios were asymmetric with respect to their maximum values; (2) the probability that the longitudinal and transverse Poisson’s ratios was within one standard deviation of their mean values were 77.2% and 61.2%, respectively.