A finite element model of semi-rigid mortise-and-tenon joint considering glue line and friction coefficient
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The aim of this study is to build a new numerical model of a mortise-and-tenon joint based on the finite element method (FEM) considering glue line and friction coefficient to analyze the semi-rigid wood joint. Firstly, the friction coefficient, glue distributions and strengths of the mortise-and-tenon joint were determined by experimental methods. Secondly, these parameters were specified to a T-shaped mortise-and-tenon joint model to build a finite element model of joint by FEM. Finally, both withdrawal and bending load capacity of T-shaped specimens were investigated by experimental and numerical methods. The results showed that the testing methods used to determine the coefficient, distributions and strengths of the glued mortise-and-tenon joint were all effective enough to determine the mechanical properties of the wood mortise-and-tenon joint, and the finite element model of joint can be applied to analyze the semi-rigid mortise-and-tenon joint with consistency beyond 85%. These methods and finite element models will contribute to the analysis of wood products and wood constructions.
KeywordsFinite element model Semi-rigid Wood framework Glue line Friction coefficient
finite element method
coefficient of variance
analysis of variation
least significant difference
Mortise-and-tenon joint is widely used in wood products and wooden constructions engineering [1, 2]. It is well known that the joints are critical part of wood frameworks [3, 4, 5]. Besides, it is a typical semi-rigid joint manufactured by wood. It was first introduced into stiffness evaluation of furniture joint by Eckelman . Generally, it is difficult to evaluate the strength of a semi-rigid joint accurately by normal knowledge of mechanics. However, with the development of computer technique, the finite element method (FEM) has been popular with engineers and applied to structure design of wooden constructions and wood products. Although a number of studies have focused on this topic, the methods of modeling a reasonable semi-rigid mortise-and-tenon joint by FEM has not been figured out.
The mortise-and-tenon joint was regarded as a rigid joint in some studies [7, 8] using FEM to analyze the skeletal furniture. Obviously, although this can simplify the model, the results were not accurate enough to analyze the whole frame of furniture. Also, others considered it as semi-rigid by taking glue line into consideration when building finite element model of joint by FEM. However, the joint is usually assumed as a clearance fit and the gap is equal to the clearance [9, 10, 11, 12]. In addition, the mortise-and-tenon joint was seen as a semi-rigid connection by adding a spring which was predefined by spring constant value . These studies contributed to analyze semi-rigid joint by FEM, but further studies must been conducted to make it more accurate. Džinčić and Živanić  studied the distributions of glue in the joint with entire clearance and total interference fit by metallographic microscope. The results showed that, with 0.1 mm clearance fit, the glue line was clear and not interrupted along the tenon, and the average thickness of joint was 0.095 mm. By contrast, with interference fit, no glue was observed but only the compressed wood, because the glue in the interference fit area was squeezed out. However, in factual industrial practice, the real-time manufacturing condition of the mortise-and-tenon joint is both with interference fit and clearance fit at the same time (i.e., the interference fit in wide direction of tenon, and clearance fit in thick direction of tenon). Thus, the distributions of glue in real-time condition should be determined, and a reasonable model of the mortise-and-tenon joint must take these points into consideration.
In this study, the concept of the semi-rigid mortise-and-tenon joint can be explanted as the effects of glue line, friction coefficient and the strength of wood itself. So it is vitally important to know more about the distributions of glue, the friction coefficient of joint and mechanical properties of wood before building the model of joint. In addition, the mechanical properties of joint inputted into the finite element model must be determined and assigned to a model with appropriate finite elements.
The aim of this study was to further investigate the distributions of glue and friction coefficient of joint considering the real-time condition of joint by experimental methods, and build a finite element model of mortise-and-tenon joint based on the results determined by experiments. In addition, a comparison was made between the results of FEM and experiment to verify the validity of the finite element model through determining withdrawal and bending resistance loading capacity of T-shaped mortise-and-tenon joint specimens.
Materials and methods
All of the specimens were made with beech (Fagus orientalis. Lipsky), bought from local wood commercial supplier (Nanjing, China). According to the ASTM D 4442 , the average density was 0.692 g/cm3, and the moisture content of beech was conditioned to and held at 10.8% before and during the experiment. Besides, the joint was glued with polyvinyl acetate (PVAc), which was produced by Pattex, and the solid content was 52%. In addition, the temperature was controlled at 22 °C, and the relative humidity was 48% during the whole process of experiment.
Friction coefficient of the joint
Shear and internal bond strength of glued joint
Distribution of glue in the joint
Fluorescence microscope (DM 50008B, Leica, Shanghai, China) was used to determine the actual distributions of glue in the joints. Toluidine blue solution with 0.5% solid content was used to stain all slices cut from block specimens (Fig. 3b, c). The glue line thickness of each specimen was measured 20 times by using Imagine J2x software.
Withdrawal and bending loading capacities
A 30 mm displacement load was imposed on the stretcher to produce withdrawal (Fig. 6a) and bend (Fig. 6b) effects on the joint model, respectively. The total reaction force obtained at the reference points (RP) were the withdrawal and bending loading capacities of the modeled joint.
Results and discussions
Friction coefficient of joint
According to the testing method shown in Fig. 4, the friction coefficient was figured out by Eq. 1. The average friction coefficient of the mortise-and-tenon joint is 0.54 with coefficient of variance (COV) 7.62%. Besides, the results were analyzed by analysis of variance (ANOVA) and all mean comparisons were performed at the 1% significance level using the protected least significant difference (LSD) multiple comparisons procedure. The results shows that the effect of grain orientations of tenon on friction coefficient is not statistically significant with p value far more than 0.01. Besides, Hu and guan  studied the influences of pressures and grain orientations on the friction coefficient of beech wood, and the results showed that the effects of pressure on the friction coefficient of wood were not considered to be statistically significant.
Distributions of glue in joint
Shear strengths of the glue joint
Comparison between the experiment and FEM
Comparison of withdrawal and bending load capacities of experiment and FEM
The method used to measure the friction coefficient of the joint is effective, and the average friction coefficient of beech wood mortise-and-tenon joint is 0.54.
The distributions of glue in the mortise-and-tenon joint can be determined by fluorescence microscope clearly. Specifically, the thickness of the glue line in the flat surface is 54.54 μm, while glue was absent in the curve surface of the joint.
The procedures applied to process the specimens and measure the shear strengths of the mortise-and-tenon joint are valid, and the difference of shear strength GI and GII is not statistically significant.
The results of the finite element model are well consistent with those of the experiments in withdrawal and bending loading capacities of the mortise-and-tenon joint T-shaped specimens.
In conclusion, the methods used in this paper can be applied to measure the distribution of glue, friction coefficient and strengths of the joint. In addition, the finite element model of the mortise-and-tenon joint can be applied to the structure design of wood furniture and wooden constructions.
All authors materially participated in the research and article preparation. Both authors read and approved the final manuscript.
The authors thank the support of a project funded by A Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
This manuscript has not been submitted to any of the other journals and has not been published previously (partly or in full). Its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out. There are no competing interests in this manuscript.
Availability of data and materials
The data are available if needed.
This work was supported by a project funded by A Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
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- 1.Tankut AN, Tankut N (2005) The effects of joint forms (shape) and dimensions on the strengths of mortise and tenon joints. Turk J Agric For 29:493–498Google Scholar
- 3.Eckelman CA (1971) Bending strength and moment rotation characteristics of two-pin moment resisting dowel joints. Forest Prod J 21(3):35–39Google Scholar
- 6.Eckelman CA (1968) Furniture frame analysis and design. PhD thesis, Purdue University, West Lafayette, INGoogle Scholar
- 7.Gavronski T (2006) Rigidity-strength models and stress distribution in housed tenon joints subjected to torsion. Wood Technol 9(4):32Google Scholar
- 8.Çolakoglu MH, Apay AC (2012) Finite element analysis of wooden chair strength in free drop. Int J Phys Sci 7(7):1105–1114Google Scholar
- 10.Silvana P, Smardzewski J (2010) Effect of glue line shape on strength of mortise and tenon joint. Drvna Ind 61(4):223–228Google Scholar
- 11.Derikvand M, Dalvand M, Maleki S, Ebrahimi G (2015) Numerical analysis of semi-rigid furniture connections using FEM. In: The XXVIITH international conference research for furniture industry. Ankara, Turkey, 17–18 September 2015, pp 28–38Google Scholar
- 13.Kılıç K, Kasal A, Kuşkun T, Acar M, Erdil YZ (2018) Effect of tenon size on static front to back loading performance of wooden chairs in comparison with acceptable design loads. BioResources 13(1):256–271Google Scholar
- 14.Džinčić I, Živanić D (2014) The influence of fit on the distribution of glue in oval tenon mortise joint. Wood Res-Slovakia 59(2):297–302Google Scholar
- 15.ASTM D 4442-92 (2001) Standard test methods for direct moisture content measurement of wood and wood-base materials. American Society for Testing and Materials, West ConshohockenGoogle Scholar
- 16.ASTM D1037 (2012) Standard test methods for evaluating properties of wood-base fiber and particle panel materials. ASTM International, West ConshohockenGoogle Scholar
- 17.CNS GB/T 1935 (2009) Method of testing in compressive strength parallel to grain of wood. China National Standard, Beijing (In Chinese) Google Scholar
- 18.Hu WG, Guan HY (2017) Study on elastic modulus of beech in different stress states. J Forest Eng 2(06):36–41 (in Chinese with summary in English) Google Scholar
- 19.Hu WG, Guan HY (2017) Investigation on withdrawal capacity of mortise and tenon joint based on friction properties. J Forest Eng 2(04):158–162 (in Chinese with summary in English) Google Scholar
- 20.Hu WG, Guan HY (2017) Experimental and numerical study on optimization design of stretcher positions. Wood Res Slovakia 62(4):575–586Google Scholar
- 21.Hu WG, Guan HY, Zhang JL (2018) Finite element analysis of tensile load resistance of mortise-and-tenon joints considering tenon fit effects. Wood Fiber Sci 50(2):121–131Google Scholar
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