Static tensile experiments and numerical simulations were carried out to study effects of hole perpendicularity error on mechanical performance of singlelap doublebolt composite joints. Hole tilting angle, varying from 1 to 4 degrees, and hole tilting direction to account for anisotropic properties of composite material were investigated. Progressive damage model (PDM) based on ChangLessard type criterion with an extension by Olmedo was created, which involved seven failure modes and made material properties be a direct function of predefined field variables. The model was implemented in ABAQUS/Standard using a UMAT subroutine. Good agreement was found when comparing numerical simulation results with experimental outcomes. In addition, the results demonstrate that, with increasing of hole tilting angle, damage is prone to arise and the load path of the composite bolted joints alters with changing of hole tilting direction, which result in severe stress concentration around the edge of hole and joint failure in advance.
Designable combinations of fiber and matrix make the composite a versatile material. Their high strength coupled with light weight leads to their use wherever structural efficiency is at a premium. However, joints are always necessary to manufacture a large composite structure, among which bonded joints become increasingly common in automotive and marine field due to their ability to improve structural performance and help weight reduction [
The main purpose of studies on composite bolted joints is to determine the effect of various parameters on joint strength. Theoretical results are also used to serve the improvement of bolted joint design and exploit the full potential of CFRP. Unsustainable and conservative design can therefore be avoided with methods that have been benchmarked against satisfactory data. The parameters that have been studied include geometrical factors [
The process factors determine the structural parameters of composites, the physicalmechanical properties, and the residual stresses produced by assembly process. Typical process factors include the bolt hole clearance effects, the accuracy and interchangeability of the joints, and the machining quality of the holes. Many factors have been studied by scholars except for hole perpendicularity error. In this paper, hole perpendicularity error is taken into consideration to enrich the study of composite bolted joints. Finite element analysis (FEA) and experiments were carried out and compared to assess the mechanical performance of composite joints.
Hole perpendicularity error is a kind of manufacturing defects, which results in stress concentration around hole edge area. In the case of singlelap singlebolt composite joint, the appearance of hole perpendicularity error will lead to bearing capability decrease of the bolted joint [
Considering the anisotropic properties of CFRP, two parameters are used to characterize the hole perpendicularity error, tilting direction
Characterization of perpendicularity error of hole from [
Only tilting directions
Patterns of singlelap doublebolt joints.
P0
P1
P2
P3
P4
P5
The specimens used in this study were manufactured from IMS194/CYCOM9772 carbon fiber/epoxy prepreg (nominal ply thickness is 0.188 mm) and designed to fail initially in the bearing mode with symmetric stacking sequence of [−45/0/45/90/0/90/45/0/−45/45
Mechanical properties of IMS194/CYCOM9772.
Elastic property  Value  Strength property  Value 


165 

3150 



1450 





4.27 







2.52 



0.33 

108 



108 

0.55 

108 
Plastic behavior of SCM35 alloy steel.
Stress/GPa  Plastic strain 

0.63  0 
0.76  0.01 
1.08  0.05 
1.13  0.08 
1.2  0.1 
Singlelap doublebolt composite joints were prepared according to the ASTM standard D5961/D5661 M13 with widthtohole diameter ratio
Configuration of specimens (unit: mm).
According to the ASTM D5961 standard, the static tensile tests were performed on a WDW100 testing machine in displacement control at a rate of 1.0 mm/min. The experimental setup is shown in Figure
Test groups and parameters.
Group  Pattern 

Repeat 

P00  P0  0  3 
P0030  P0  0  1 
P14  P1  4  3 
P1430  P1  4  1 
P22  P2  2  3 
P24  P2  4  3 
P2430  P2  4  1 
Experimental setup.
To investigate the effects of hole perpendicularity error on mechanical behavior of singlelap doublebolt composite joints, a nonlinear threedimensional finite element model was constructed with 8node solid element C3D8R using the commercial finite element software, ABAQUS [
FEA model and interactions of bolted joint.
To reduce the computational cost, the grip area of the composite laminate was neglected and the laminate was modelled with 5 elements in thickness direction, which avoids excessive widthtothickness ratio of the element [
Contact interactions between all surfaces were modelled by surfacebased contact considering the linear penalty method. Seventeen contact interactions with finite sliding formulation were defined to simulate the interfaces between any two parts. The stiffness of master surface was relatively larger and the meshes were designed to be coarser than those of slave surfaces. Default contact control and contact stabilization were defined for each contact pair to improve convergence. Constant value of friction coefficient was set to 0.3 [
Boundary conditions were applied to reference points, which defined coupling constraints to node sections in the FEA model as shown in Figure
There were 42,272 elements in total in the finite element model. Considering that the region around the hole is the key area of stress concentration, the size of refined meshes was approximately 0.36 × 0.77 mm in the vicinity of the hole in order to ensure the accuracy. Coarser meshes were adopted further to reduce computational cost. The element size of bolts and washers was set up corresponding to the size of the contact areas of the laminates.
The progressive damage method has attracted extensive attention in analysis and design of composite structures, which effectively simulates damage formation, evolution, and ultimate failure process of complex composite structures. Unlike isotropic materials, the destruction of composite materials is a gradual process. The progressive damage method is based on damage mechanics, which regards the failure of composite materials as damage. The material degradation model was used to describe the mechanical behavior of damaged material.
The progressive damage analysis includes the stress solving of the nonlinear finite element equilibrium equation, the prediction of damage initiation, damage evolution, and the stiffness degradation based on the material failure criterion. Stress analysis is mainly carried out by finite element software and has evolved from twodimensional model into threedimensional model. There are diverse failure criteria to predict the damage initiation including Chang criteria [
Tensile fiber failure,
The composite laminates are subjected to gradual increasing load. Once the stress matches the equations of failure criteria, damage occurs. The mechanical properties of the material elements in the damaged area will be degenerated with a sudden drop and the degradation rules are given in Table
Material property degradation for each failure criterion.
Model of failure  Material properties degradation rules 

Matrix cranking failure 

Matrix crushing failure 

Tensile fiber failure 

Compressive fiber failure 

Fibermatrix shearout failure 

Delamination onset in tension 

Delamination onset in compression 

There are no acknowledged degradation criteria of material property. Most of them are determined based on experiments and experience. The sudden drop degradation model is relatively easy to implement and thus is widely used in the progressive damage analysis of composites. Tan [
Figure
Comparison of numerical and experimental load–displacement curves.
As shown in Table
The experimental and numerical bearing behaviors of all specimens.
Group  Stiffness 
Mean 
Ultimate load 
Mean 

P00  33289  30711  38206  38047 
P00  30424  38568  
P00  28421  37367  
P14  31889  31181  37800  37734 
P14  30964  37668  
P14  30691  37976  
P22  26500  28083  38894  37450 
P22  28673  37783  
P22  29076  35671  
P24  27171  26540  37964  37745 
P24  25804  37526  
P24  26645  37535  
FEAP0  —  36690  —  35900 
Figure
Failure morphology of the top laminate under failure load.
Damage envelope of various failure modes under ultimate load.
Tensile fiber failure (SDV1)
Compressive fiber failure (SDV2)
Tensile matrix failure (SDV3)
Compressive matrix failure (SDV4)
Delamination onset in tension (SDV5)
Delamination onset in compression (SDV6)
Fibermatrix shearout failure (SDV7)
Bearing failure of composite laminate is a combination of multiple damage occurrences. When subjected to tensile loading, the bolt shank is pressed against the bolt hole. Then, the fibers firstly bear the load due to their larger elastic modulus and are gradually buckling as the load increases until fracture. After that, matrix compression failure and fibermatrix shearout failure occur along with delamination between layers. Gradually, as fiber and matrix failures continue to expand, the loadcarrying capacity of the composite laminates decreases.
In this section, how the load
The stiffness and ultimate load of FEA results.
Group  Stiffness/N/mm  Decline/%  Ultimate load/N  Decline/% 

P0  26515  —  35901  — 


P11  26325  0.72  35552  0.97 
P12  26061  1.71  35336  1.58 
P13  25751  2.88  34901  2.79 
P14  25187  5.01  33394  6.98 


P21  25154  5.13  35077  2.30 
P22  23389  11.79  35052  2.36 
P23  21805  17.76  34419  4.13 
P24  21482  18.98  33302  7.24 


P31  25327  4.48  35506  1.10 
P32  23453  11.55  35353  1.53 
P33  22015  16.97  34088  4.28 
P34  22005  17.01  33182  7.57 


P41  25090  5.4  35558  0.96 
P42  20203  23.8  35429  1.31 
P43  16926  36.2  34675  3.41 
P44  15501  41.5  33441  6.85 


P51  26161  1.3  35388  1.43 
P52  23667  10.7  35453  1.25 
P53  23185  12.5  35013  2.47 
P54  21140  20.3  32830  8.55 
Numerical results of hole perpendicularity error on joint performance.
P1
P2
P3
P4
P5
Comparison of different joint patterns
As shown in Figure
Figure
The influence of hole tilting direction on joint stiffness.
The appearance of hole perpendicularity error will alter the load transfer path and affect loads transferred by laminates in a singlelap doublebolt joint. The expectant result is obviously that more elements are damaged around the bolt hole when it bears more load. Take tensile load of 30 kN as an example and numerical results of matrix crushing damage are given in Figure
Load transfer path and damage of matrix crushing failure.
To prove the above conclusion, specimens loaded up to 30 kN, about 80% of the ultimate load, were disassembled to observe the damage around the holes. Pictures captured by optical microscope are shown in Figure
Hole damage pictures for specimen loaded up to 30 kN.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (Grant nos. 51375068 and 51475073), the Major State Basic Research Development Program (Grant no. 2014CB046504), the Fundamental Research Funds for the Central Universities (Grant no. DUT17JC19), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.