High-temperature effect on the mechanical performance of screwed CFRPI–TC4 alloy joints repaired with metal inserts

Abstract

This paper seeks to study high-temperature effect on mechanical performance of screwed single-lap carbon fiber-reinforced polyimide–TC4 titanium alloy joints repaired with metal inserts. Quasi-static tension tests were conducted at room temperature (RT) and 250℃ to determine the joint strength and stiffness of repaired joints with metal inserts. Based on the experimental results, high-temperature effect on joint strength and stiffness and insert repair efficiency were analyzed and discussed. A new analytical model was established to evaluate the effect of high temperature on joint stiffness. It is concluded that (1) joint strength and stiffness for all configurations are lower at 250℃ than that at RT, showing the expected detrimental effect of high temperature on joint strength and stiffness. The reductions in joint strength and stiffness depend on the joint configuration; (2) the repair efficiencies of embedded conical nut for joint strengths of protruding and countersunk head screw joints decrease, but those for joint stiffness increase at 250℃ as against at RT. Unlike the repair efficiencies of embedded conical nut, the repair efficiency of bushing for joint strength is slightly greater, but that for joint stiffness is less at 250℃ than at RT; and (3) the developed analytical model is capable of predicting the displacement of screwed single-lap carbon fiber-reinforced polyimide–TC4 joints at RT and high temperature, and there is good agreement between the experimental data and the predicted curves.

Keywords

Carbon fiber-reinforced polyimide–TC4 joints high temperature metal insert repair joint strength joint stiffness

Introduction

With persistent efforts on light-weight design of aircraft engine structures (operating temperatures often exceed 250℃), carbon fiber-reinforced polyimide (CFRPI) and titanium (Ti) alloys have been largely applied because of their high specific strength and stiffness, and especially high-heat-resistant properties. Due to the high assembly and repair efficiency, low requirements for surface treatment and good compatibility between CFRPI materials and Ti alloys, mechanically fastened CFRPI–Ti alloy joints are more favorable as compared with the corresponding bonded joints in aircraft engine structures.¹ Meanwhile, the screws are often used to tighten the fastener from only accessible one side of the structure with a smoother surface.² Thus, the high-temperature performances of the screwed CFRPI–Ti alloy joints are of great concern in the design and repair of aircraft engine structures.

At room temperature (RT), mechanical performances of screwed CFRPI–Ti alloy joints depend on many factors including material properties of plate and fastener,³ joint geometry and dimensions,⁴ manufacturing and assembly process such as clearance, clamping force, friction coefficient of assembly surface, and location error of fastener hole.^5,6 Moreover, the hole-edge is inevitably damaged during the process of hole drilling, and the inner thread of the Ti alloy plate is always frayed during repetitive installation for repair or inspection, which also immensely affect mechanical performances. In general, mechanically fastened joints present several typical failure modes such as net tension, shear-out, bearing, tear-out and cleavage (shown in Figure 1), and the bearing failure is the commonest among these failure modes.⁷ In order to assure structural integrity of mechanically fastened joints, bonded metal inserts are usually applied to repair the bearing damage around the hole because of the low cost and high repair efficiency (shown in Figure 2).^8,9

Figure 1.

Failure modes of bolted joint. (a) net-tension; (b) shear-out; (c) bearing; (d) tear-out and (e) cleavage.²⁵

Figure 2.

Bonded metal inserts to repair mechanically fastened joints.⁹

It is understood that high temperature generally poses the resin softening, the degradation in fiber/resin interface strength of the composite plate, the reduction in adhesive strength between inserts and plates, and the altering in stress pattern near the fastener hole.^10–12 Meanwhile, the difference of thermal expansion coefficient between the joint members often triggers greater radial thermal stress on the contact interface and severer relaxation of clamping stress at high temperature than at RT,^13,14 ultimately decreasing the carrying capacity and repair efficiency of metal inserts for mechanical performances of joints.

Several analytical models have devised to evaluate mechanical performances of the bolt/nut joints. Rosenfeld¹⁵ proposed a mass-spring model for double-lap joints made of isotropic materials, and Nelson et al.¹⁶ extended the mass-spring model to the joints made of anisotropic materials. Based on the mass-spring model, by considering the static friction force between plates and the elimination process of the clearance, McCarthy et al.¹⁷ and McCarthy and Gray¹⁸ developed a bi-linear model and a tri-linear model to understand the effects of bolt-hole clearance and bolt torque on mechanical performances of single-column multi-bolt composite joints, and the earlier stages on the load–displacement curves were predicted. Olmedo et al.¹⁹ further modified the mass-spring model to analyze the effect of joint parameters on the joint stiffness of single-lap composite joints, by accounting for the effects of secondary bending of plate. Again, Kou et al.²⁰ presented a four-stage model for single-lap torque bolted-joint to predict the non-linearity of load–displacement curves, by considering the partial slip process between plates and the relationship between bearing stress and clearance.

From the previous reviews, it is clear that most of the research has been focusing on mechanical performances of screwed joints with insert repair at the temperatures ranged from RT to 200℃ because the glass transition temperature $T_{g}$ for epoxy matrix composite is generally lower than 200℃. Little quantitative results can be found in literature for mechanical performances of screwed joints with insert repair at a higher temperature than 200℃ (e.g. 250℃), particularly there seems to be precious few works done on the synergistic interaction between high temperature and screw tilt bearing on the mechanical performances of screwed CFRPI–Ti alloy joints with insert repair, which is the focus of this paper.

Experimental procedures

Due to the superior mechanical properties at high temperature and widespread application in aircraft structures, unidirectional CCF300/AC721 carbon fiber/polyimide composite and TC4 Ti alloy (e.g. Ti-6Al-4V) were selected to fabricate the screwed single-lap joints investigated here, and 30CrMnSiA alloy steel screw was used to join CFRPI and TC4 plates. As almost same as the T300 carbon fiber, CCF300 is a kind of polyacrylonitrile-based carbon fiber from WeiHai TuoZhan fiber Co. Ltd. in China, while AC721 is a Chinese-made autoclave molding polyimide with a higher glass transition temperature than 350℃ and a higher decomposition temperature than 500℃.^21,22 The ply stacking sequence of the CCF300/AC721 CFRPI laminate is [45/0/0/−45/90/0/45/0/−45/90/0/45/0/−45/90/0]_s (32 layers), and the basic material properties are listed in Table 1. The geometry and dimensions of screwed single-lap CFRPI–TC4 joint are shown in Figure 3(a), and the ratios of width to diameter and edge-distance to diameter were designed to be 6 (here $30 / 3055 = 6$ ) and 3 (here $15 / 1555 = 3$ ), respectively.²³ Additionally, phenolic resin doublers with the thicknesses of 4 mm and 5 mm were bonded on grip area (shown in Figure 3(a)) prior to static strength test, and the size of screw is M5, and the radii of screw shank and screw head are 2.5 mm and 4.3 mm, respectively. The clearance between the screw shank and the composite hole is 0.1 mm.

Figure 3.

Geometry and dimensions of screwed single-lap CFRPI–TC4 joint and TC4 inserts. (a) Screwed single-lap CFRPI-TC4 joint; (b) Embedded conical nut and (c) Bushing.

Table 1.

Mechanical properties of joint materials.

Materials	Properties	Mean values
Materials	Properties	RT	250℃
CCF300 carbon fiber	Longitudinal CTE/ $10^{- 6} \cdot \circ C^{- 1}$	−0.6 (From RT to 250℃)
CCF300 carbon fiber	Transverse CTE/ $10^{- 6} \cdot \circ C^{- 1}$	8.5 (From RT to 250℃)
AC721 polyimide	CTE/ $10^{- 6} \cdot \circ C^{- 1}$	30 (From RT to 250℃)
UD CCF300/AC721 composite	Longitudinal modulus/GPa	127	116
	Transverse modulus/GPa	9.4	4.6
	Major Poisson's ratio	0.3	0.3
	In-plane shear modulus/GPa	4.6	2.3
	Out-of-plane shear modulus/GPa	4.6	2.3
TC4 titanium alloy	Tensile strength/GPa	967	715
	Young's modulus/GPa	109	91
	Shear modulus/GPa	40	35
	CTE/ $10^{- 6} \cdot \circ C^{- 1}$	9.3 (From RT to 250℃)
30CrMnSiA alloy steel	Tensile strength/GPa	1205	1005
	Young's modulus/GPa	196	172
	Shear modulus/GPa	75.5	66.2
	CTE/ $10^{- 6} \cdot \circ C^{- 1}$	12.9 (From RT to 250℃)

RT: room temperature; CTE: coefficient of thermal expansion.

Two kinds of metal inserts (i.e. embedded conical nut and bushing) made of TC4 Ti alloy were fabricated to repair the hole-edge damage of the CFRPI and TC4 plates, respectively. The geometry and dimensions are shown in Figure 3(b) and (c). In order to investigate the repair efficiency, screwed single-lap CFRPI–TC4 joints of six fastener configurations (or configurations P0, P1, C0, C1, C2, and C3) were fabricated (shown in Table 2). Configurations P0 and P1 used a protruding head screw, while configurations C0–C3 used a countersunk head screw. The bushing was used in configurations P1 and C1. An embedded conical nut was used in configuration C2, while a bushing and an embedded conical nut were combined in configuration C3. The bushing and the embedded conical nut were bonded to the fastener hole of the CFRPI plate and the TC4 plate by using a RT curing epoxy resin adhesive and the shear strength at RT is 3 MPa. In order to prevent the adhesive from permeating into the contact surface, we firstly applied the adhesive evenly on the insert surface, then assembled the inserts with the corresponding plate, and finally assembled the CFRPI plate and TC4 plate after curing of the adhesive. In addition, because the tightening torque of the screw significantly affects joint strength and stiffness, a torque wrench was used to tighten the screw with a fixed torque of 3.6

N \cdot m

. At least three valid data were required for each quasi-static tensile test, implying 36 valid data for all configurations at each temperature.

Table 2.

Screwed single-lap CFRPI–TC4 joints.

Fastener configurations		P0	P1	C0	C1	C2	C3
Sketches
Screw types		M5 Protruding head		M5 Countersunk head
Metal inserts		–	Embedded conical nut	–	Embedded conical nut	Bushing	Bushing & Embedded conical nut
Holes	CFRPI	Straight (Φ5)		Countersunk (Φ5)		Straight (Φ10)
Holes	TC4	Threaded (Φ5)	Taper (Φ12)	Threaded (Φ5)	Taper (Φ12)	Threaded (Φ5)	Taper (Φ12)

CFRPI: carbon fiber-reinforced polyimide.

Quasi-static tension tests at RT were conducted on an INSTRON-8803-50KN servo-hydraulic machine, while quasi-static tension tests at 250℃ were conducted on a QBS-100 kN servo-hydraulic machine, and a SDGDYD−180/+350 environmental chamber whose temperature fluctuated within ±2℃ was employed to maintain the testing temperatures of 250℃ through controlling the electromechanical heater of the environmental chamber (shown in Figure 4(a)). Due to the great size of the hydraulic grip system, it is hard to install the hydraulic grip system in the environmental chamber, and the test fixture was then used to grip the joint specimen (shown in Figure 4(b) and (c)). From Figure 4(b) and (c), it is clear that four fastening holes and one centering hole were manufactured on the test fixture, and the specimen was first fixed on the test fixture through the centering rods and then gripped and clamped by tightening the bolts. In order to make sufficient clamping and friction forces on the joint specimen for transferring the tension or compression loading, the circular arc grooves were fabricated at the root of test fixture to reduce the stiffness of grip for increasing the clamping force, and the knurling grip surfaces were manufactured to increase the roughness for increasing the friction factor (shown in Figure 4(c)). For these reasons, we argue that the test fixture transfers the axial loading by sufficient clamping and friction forces on the joint specimen, but not by pin-loading. For the tests at 250℃, the unloaded specimen was firstly gripped and clamped by the test fixture, and then the temperature of the environmental chamber was increased to 250℃. After the temperature inside the environmental chamber reached 250℃, it was maintained for 30 min to ensure the temperature within the whole specimen was uniform and stable. In order to avoid premature failure caused by thermal expansion, the test machine was set to output “zero loads” to the specimen during the temperature rise and maintaining period. Quasi-static tension load was continuously applied to specimens to produce failure within 10 min, during which the load–global displacement data were recorded.

Figure 4.

Static strength test of joint at high temperature. (a) Test setting; (b) Specimen installation and (c) Test fixture.

Figure 5 shows the load–displacement curves for all configurations at RT and 250℃. From Figure 5, it is obvious that the load–displacement curves for all configurations at RT and 250℃ present five typical stages: no-slip, slip, full-contact, damage onset and growth, and final failure (see Figure 6), and the characteristics and mechanisms for each typical stage on the load–displacement curves are summarized and shown in Table 3. However, the no-slip and slip stages on the load–displacement curves of configurations C2 and C3 seem more invisible at 250℃ than at RT. This is due to the fact that the coefficient of thermal expansion (CTE) for 30CrMnsiA alloy steel is greater than that of TC4 (see Table 1). The CTE difference decreases the clearance between screw shank and hole surface as well as the preload of screw with the increase in temperature, causing invisible slip stage on the load–displacement curves.

Figure 5.

Load–displacement curves for joints of six configurations at RT and 250℃. (a) Configuration P0; (b) Configuration C0; (c) Configuration P1 and (d) Configuration C1; (e) Configuration C2 and (f) Configuration C3.

Figure 6.

Five stages on load–displacement curves at RT.

Table 3.

Characteristics and mechanisms of representative stages on load–displacement curve.

Stages	Characteristics	Mechanisms
(i) No-slip	At initial stage, linear relation exists between load and displacement	Load transfer between plates is via static friction, and the change in displacement of joint results from elastic deformation of plates.
(ii) Slip	A short plateau region with a significant decrease in the slop of curve	Relative slip appears between plates, increasing additional displacement and causing a near-zero joint stiffness.
(iii) Full-contact	A long linear region with an increasing slop as compared to the slip region	The interface between the screw and fastener hole is in full-contact, and the load transfer between plates is conducted through the bearing stress around the hole.
(iv) Damage onset and growth	A long and locally instable region with a distinct slop reduction	The bearing damage around the hole (or in the screw) occurs and propagates with the increase in the tensile load, leading to a progressive reduction in joint strength and stiffness.
(v) Final failure	The load capacity of the joint declines	Screw failure (or bearing failure on CFRPI plate) appears.

CFRPI: carbon fiber-reinforced polyimide.

Table 4 presents the experimental results of joint strength and stiffness for all configurations at RT and 250℃. From Table 4, it is evident that the joint strength and stiffness for all configurations are lower at 250℃ than that at RT, showing the expected detrimental effect of high temperature on joint strength and stiffness. The reductions in joint strength and stiffness at high temperature depend on the joint configuration. The mean values of static tensile strength for configurations P1 and C2 at 250℃ are, respectively, about 44.4% and 14.7% lower than those at RT, which are the largest and lowest reductions in static tensile strength. Nevertheless, the mean values of static tensile stiffness for configurations P0 and C1 at 250℃ are respectively about 29.7% and 14.3% lower than those at RT, which are the largest and lowest reductions in static tensile stiffness.

Table 4.

Experimental results of tension strength for joints of six configurations.

Configurations	Temperatures	Number of specimens	Strength/kN		Stiffness/kN/mm		Damage modes
Configurations	Temperatures	Number of specimens	Mean/kN	Relative deviation (%)	Mean/kN/mm	Relative deviation (%)
P0	RT	5	7.2	–	9.1	–	I
P0	250℃	5	5.3	26.4	6.4	29.7	I
P1	RT	5	8.1	–	7.0	–	I
P1	250℃	5	4.5	44.4	5.7	18.6	I
C0	RT	5	8.8	–	8.1	–	I
C0	250℃	5	7.4	15.9	6.6	18.5	I
C1	RT	5	8.7	–	7.0	–	I
C1	250℃	5	7.0	19.5	6.0	14.3	I
C2	RT	4	9.5	–	9.5	–	II
C2	250℃	5	8.1	14.7	7.4	22.1	II
C3	RT	4	9.2	–	8.9	–	II
C3	250℃	5	7.5	18.5	7.5	15.7	II

RT: room temperature.

From the experimental observation, two kinds of bearing damage mode (i.e. modes I and II) at the hole-edge of CFRPI plate were found to lead to the screw failure of joints at RT and 250℃ (shown in Figure 7 and Table 4). The bearing damage mode I is the hole elongation, manifesting an evident non-uniform bearing characteristic in the through-thickness direction, while the bearing damage mode II is the bearing failure of 45° layer on the surface of composite laminate. The screw tilt effect is probably the main reason resulting in the different bearing damage modes.

Figure 7.

Two kinds of bearing damage along the CFRPI hole-edge. (a) Damage mode I and (b) Damage mode II.

Results and discussion

Table 4 shows that all joint strength and stiffness for configurations P0 and C0 without inserts are much lower at the high temperature than at RT. However, the reductions in joint strength and stiffness are larger for configuration P0 than for configuration C0, implying that configuration P0 is more sensitive to high temperature than configuration C0. And thus, we conclude that the detrimental influence of high temperature is dependent on screw type of joint. In reality, the high-temperature softening of resin and the CTE mismatching between resin and fiber greatly weaken mechanical properties of resin and fiber/resin interface strength, ultimately degrading composite laminate, especially the ±45° and 90° layers. Moreover, both static strength and stiffness of 30CrMnSiA alloy steel and TC4 Ti alloy have distinct reduction at high temperature (as listed in Table 1), significantly increasing the deformations and immensely decreasing the strength of screw and TC4 plate.²⁴ As a result, high temperature fundamentally decreases the joint strength and stiffness.

Although the bearing damage modes for configuration P0 and C0 at RT and 250℃ follow mode I (see Table 4), the load-transferring mechanism for both configurations are different from each other. Actually, the bearing stresses mainly act on the straight part of screw (rather than the countersunk head part) for configuration C0, but on the screw head part for configuration P0, deducing less secondary bending moment for configuration C0 than for configuration P0 (see Figure 8). Therefore, the bearing damage mode II is dominant failure mode for configuration C0, whereas the bearing damage mode I is primary failure mode for configuration P0. The reason for this is that the screw tilt effect substantially alters the effective bearing area and stress pattern.²

Figure 8.

Bearing condition at hole-edge. (a) Configuration P0 and (b) Configuration C0.

In terms of experimental results of stiffness and strength, the repair efficiency of inserts can be evaluated as

\begin{matrix} η_{k} = \frac{K_{1}}{K_{0}} \times 100 % \\ η_{s} = \frac{S_{1}}{S_{0}} \times 100 % \end{matrix}

(1)

In accordance with equation (1) and experimental results of joint stiffness and strength (listed in Table 4), the repair efficiency of two kinds of inserts are evaluated (listed in Table 5). From Table 5, it is possible to induce the deductions as follows.

The repair efficiencies of embedded conical nut for the strength of protruding and Countersunk head screw joints decrease at 250℃ as against at RT, but those for the stiffness increase. One reason for this is that due to the material softening and viscosity reduction of adhesive layer at 250℃, under the preload of the screw, the embedded conical nut is possibly wedged into the upper end of taper hole (shown in Figure 9), decreasing the clearance between the nut and tapper hole and hereby strengthening the screw tilt constraint. The enhancement of screw tilt constraint seems helpful for joint stiffness but detrimental for secondary bending moment, bearing stress and joint strength.

The repair efficiency of bushing for joint strength is slightly greater at 250℃ than at RT, but that for joint stiffness is less at 250℃ than at RT. The reason for this is that at RT, TC4 Ti alloy has superior plasticity as compared to the CFRPI, and the local yielding of bushing at the hole-edge can relieve the stress concentration in the contact zone, slightly retarding the screw yielding and increasing the joint strength. Meanwhile, the bushing is used to fix the bearing surface of the CFRPI plate perpendicular to the direction of shear load, notably reducing the bearing deformation and enhancing the joint stiffness. In contrast, at 250℃, the plasticity of TC4 Ti alloy increases to further relieve the stress concentration between the screw shank and the bushing hole, apparently increasing screw failure load and joint strength. On the other hand, the material softening and viscosity reduction in adhesive layer at 250℃ likely trigger the interface clearance between the bushing and the CFRPI hole, drastically reducing the joint stiffness.

Like the repair efficiencies of embedded conical nut, the repair efficiency of embedded conical nut and bushing for joint strength is less at 250℃ than at RT, but that for joint stiffness is greater. This implies that the influence of embedded conical nut is more dominant for joint strength and stiffness than the bushing, and the screw tilt has an effect on mechanical performances of screw joints.

Figure 9.

Axial wedging movement for embedded conical nut.

Table 5.

Experimental results of tension strength for repaired joints.

Insert types	Screw types	$η_{s}$ /%		$η_{k}$ /%
Insert types	Screw types	RT	250℃	RT	250℃
Embedded conical nut	Protruding head screw	112.5	84.9	76.9	89.1
Embedded conical nut	Countersunk head screw	98.9	94.6	86.4	90.9
Bushing	Countersunk head screw	108.0	109.5	117.3	112.1
Embedded conical nut and bushing	Countersunk head screw	104.6	101.4	109.9	113.6

RT: room temperature.

Analytical model for evaluating joint stiffness

The displacement of screwed single-lap joint subjected to shear load always includes the tensile and secondary bending deformations of plates, shear deformation of plate at the contact zone, clearance and relative displacement between screw shank and hole. In order to establish the analytical model for evaluating the deformations of screwed single-lap CFRPI–TC4 joints, fundamental assumptions made in this paper are as follows.

Since the secondary bending deformations of joint plates are independent on the in-plane deformation, the plate lengths are much larger than the thicknesses, and the contact area between plates is much less as compared to whole area of plate;¹⁸ the joint is simplified as two Euler beams connected with concentrated forces at contact zone; and the screw is thought as the rigid body without bending or shear deformation for evaluating the secondary bending deformations of the plates.

According to foundation stiffness theory,²⁵ the contact between screw shank and hole-edge is modeled as the short beam supported by an elastic foundation, and the bearing zone around the hole-edge is regarded as the triangular shape depicted by using the screw tilt angle and the side length of triangular zone for evaluating shear deformation of plate at contact zone. At the hole-edge of plates, the distributed bearing load on bearing surface in through-thickness direction is expressed as

q (z) = kms

(2)

with

k = \frac{E}{0.8} (1 - \frac{D}{W})

(3)

where m is usually taken as 0.6.²⁶

Because of the complexity of contact and bearing between screw head and plate hole for countersunk head screwed joints, the analytical model is suitable only for protruding head screwed joints, rather than for countersunk head screwed joints.

Based on Assumption (1), the internal axial force and bending moment of joint plates are written as

N (x) = F 0 \leq x \leq 2 L

(4)

M (x) = \begin{matrix} M_{0} + P_{0} x & 0 \leq x \leq L \\ M_{0} + P_{0} x + \frac{1}{2} F (t_{1} + t_{2}) & L < x \leq 2 L \end{matrix}

(5)

From engineering beam theorem, it is possible to have the deformation compatibility conditions: the bending deformation angles at the ends of both beams are equal each other, and the bending deflection at the ends of both beams are also equal each other, namely

\begin{matrix} ϕ_{1} (L) = - ϕ_{2} (L) \\ y_{1} (L) = y_{2} (L) \end{matrix}

(6)

Again, based on engineering beam theorem, solving equations (4) to (6) shows

\begin{matrix} M_{0} = - \frac{1}{2} \frac{n^{2} - 5 n}{n^{2} + 14 n + 1} (t_{1} + t_{2}) F \\ P_{0} = - \frac{6 n}{n^{2} + 14 n + 1} (t_{1} + t_{2}) \frac{F}{L} \end{matrix}

(7)

with

n = \frac{E_{2} I_{2}}{I_{1}}

(8)

Therefore, from equations (4), (5), and (7), it can be shown the bending deformation of joint to be

\begin{matrix} δ_{a} (F) = \frac{FL}{E_{1} t_{1} W} + \frac{FL}{E_{2} t_{2} W} - \frac{2 M_{0} L + P_{0} L^{2}}{2 E_{2} I_{2}} \frac{(t_{1} + t_{2})}{2} \\ = \frac{FL}{W} (\frac{1}{E_{1} t_{1}} + \frac{1}{E_{2} t_{2}}) + \frac{1}{4} (t_{1} + t_{2})^{2} \\ \times \frac{n^{2} + n}{n^{2} + 14 n + 1} \frac{FL}{E_{2} I_{2}} \end{matrix}

(9)

No-slip stage

Static friction force on the interface between the composite and metal plates generally induces the shear deformation of plate as follows²⁰

\begin{matrix} δ_{b} (F) = \frac{\frac{t_{1}}{G_{1}} + \frac{t_{2}}{G_{2}}}{π ({R_{2}}^{2} - R_{1}^{2})} \int_{0}^{F} (1 - \frac{F}{μ N_{0}}) - \frac{2}{3} d F, F \leq μ N_{0} \end{matrix}

(10)

with

N_{0} = \frac{T_{0}}{0.4 \times R}

(11)

where μ can be selected as 0.2.^7,27

Slip stage

In slip stage, the clearance between screw shank and hole-edge of composite plate is the dominant displacement and can be written as

δ_{b, I} \leq δ_{b} (F) \leq δ_{b, I} + \frac{c}{2}

(12)

where c is equal to

2 (R_{1} - R)

Full-contact stage

Owing to the screw tilt, the contact occurs between the screw and hole-edges (see Figure 10), and the bearing displacement between the screw and hole-edge is

δ_{b} (F) = δ_{b, II} + (t_{1} + l_{1} + l_{2, f}) ϕ

(13)

Figure 10.

Bearing condition on screw-hole.

Based on the geometrical relation as shown in Figure 10, the side length of triangular zone at hole back corner in metal plate can be deduced as

l_{2, b} = t_{2} - l_{2, f}

(14)

Again, from the geometrical relation as shown in Figure 10, Assumption (2), and equations (1) and (2), it can be shown that

\begin{matrix} q_{1} (z) = m k_{1} (l_{1} - z) ϕ, & (z \leq l_{1}) \end{matrix}

(15)

From equation (15), the resultant force on composite plate is derived as

F_{1} = \int_{0}^{l_{1}} q_{1} (z) d z = \frac{1}{2} l_{1}^{2} m k_{1} ϕ

(16)

By means of force equilibrium, it is possible to have

F - μ N_{0} = F_{1}

(17)

By analogy aid of equation (16), one has

\begin{matrix} F_{2, b} = \frac{1}{2} l_{2, b}^{2} m k_{2} ϕ \\ F_{2, f} = \frac{1}{2} l_{2, f}^{2} m k_{2} ϕ \end{matrix}

(18)

In light of the bearing equilibrium condition between screw and metal plate hole, ones have

\begin{matrix} F_{2, f} - F_{2, b} = F - μ N_{0} \\ \begin{matrix} F_{2, f} (\frac{t_{2}}{2} - \frac{1}{3} l_{2, f}) + F_{2, b} (\frac{t_{2}}{2} - \frac{1}{3} l_{2, b}) \\ + μ N_{0} \frac{t_{2}}{2} = - (M_{0} + P_{0} L) \end{matrix} \end{matrix}

(19)

Substituting equation (18) into equation (19) leads to

\begin{matrix} l_{2, f} = \frac{t_{2}}{2} + \frac{F - μ N_{0}}{m k_{2} ϕ t_{2}} \\ l_{2, b} = \frac{t_{2}}{2} - \frac{F - μ N_{0}}{m k_{2} ϕ t_{2}} \\ \begin{matrix} \frac{t_{2}^{3}}{6} ϕ^{3} + \frac{2 (M_{2} + PL + μ N_{0} \frac{t_{2}}{2})}{m k_{2}} ϕ^{2} - \frac{2}{3} \frac{(F - μ N_{0}) 3}{m^{3} k_{2}^{3} t_{2}^{3}} = 0 \end{matrix} \end{matrix}

(20)

From equation (20), the screw tilt angle and the side length of triangular zones can be analytically solved, and the bearing displacement between the screw and hole-edge at RT is thus determined from equation (13). Finally, the displacement of joint at RT is obtained by using equations (9), (10), (12), and (13), and the load–displacement of joint at RT is also attained.

It is well-known that high temperature usually degrades mechanical properties of joint materials and alters the clamping force and the clearance of joint owe to CTE mismatching between the screw and composite laminate. The change in clamping force and clearance due to CTE mismatching are, respectively

Δ N_{0} = E_{3} π (R_{2}^{2} - R_{1}^{2}) (α_{2, z} - α_{s}) Δ T

(21)

Δ c = (R_{1} α_{2, x} - R α_{s}) Δ T

(22)

Similarly, by using equations (9), (10), (12), and (13) together with equations (21) and (22), the load–displacement of joint at high temperature is obtained. From the aforementioned model, it is apparent that mechanical performance of screwed single-lap joint is dependent on many factors (including material properties, joint geometry and dimensions (e.g. length and thickness of plate, ratio of width to diameter, etc.), manufacturing and assembly process (e.g. clearance, tightening torque, and friction coefficient of assembly surface)).

Based on mechanical properties of joint materials (listed in Table 1) and the geometry and dimensions of joint (shown in Figure 3(a)), the load–displacement curves at RT and 250℃ are analytically predicted from the aforementioned analytical model (shown in Figure 11). From Figure 11, we draw the following inferences. (1) At both temperatures, there is good agreement between the experimental data and the predicted curves, demonstrating that the developed analytical model is capable of predicting the displacement of screwed single-lap CFRPI–TC4 joints; (2) the accuracy of proposed analytical model at the slip stage is inferior to those at other stages. One reason for this is that the friction between screw shank and plate hole has not been considered in the proposed model. In practice, the friction between screw shank and plate hole is capable of increasing joint stiffness and load-bearing capacity;²⁸ and (3) the analytical results of joint stiffness in no-slip stage is 35.1% lower at 250℃ than at RT, whereas those in full-contact stage is 20.2% lower at 250℃ than at RT. The effect of high temperature on joint stiffness is mainly attributed to the degradation in mechanical properties of joint plates. The degradation in interlaminar shear stiffness of composite laminate is the key factor to affect the joint stiffness and load-bearing capacity in no-slip stage, while the softening in in-plane longitudinal modulus of composite and metal plates are the primary reason for the reduction in joint stiffness and load-bearing capacity in full-contact stage. As mentioned above, the glass transition and decomposition temperatures for the AC721 polyimide are higher than the test temperature of 250℃, so it is argued that no heat damage exists in the composite joint during the test and the degradation of mechanical performances of joint can be restored. To validate this argument necessitates more experimental results, which forms the basis for some further investigation.

Figure 11.

Load–displacement curves from experiments and predictions. (a) Room temperature; (b) 250℃ and (c) Comparison between predicted curves at RT and 250℃.

Figure 12(a) to (f) shows the effects of geometric dimensions and manufacturing and assembly on mechanical performances of joints. The results in Figure 12 lead to the following deductions: (i) the increase in plate length decreases joint stiffness, which is in accordance with the literature.¹⁹ This is due to the increase in secondary bending angle of plate; (ii) the increase in the ratio of width to diameter increases joint stiffness. This owes to the increase in bearing stiffness of hole-edge; (iii) the increase in the thickness of metal plate increases joint stiffness, and this is probably since the increase in the thickness of metal plate enhances the constraint of screw tilt; (iv) the increase in the clearance between screw shank and plate hole of composite plate has negligible impact on join stiffness, but significantly increases the slip displacement in stage II; and (v) both screw tightening torque and friction coefficient of assembly surface have significant influence on joint stiffness and load–displacement curve.

Figure 12.

Effect of joint geometric dimensions and manufacturing and assembly. (a) Plate length effect; (b) Effect of ratio of width to diameter; (c) Effect of plate thickness ratio; (d) Effect of clearance of composite plate hole; (e) Effect of screw tightening torque and (f) Effect of friction coefficient.

Conclusions

This paper presents an investigation about the effect of high temperature on mechanical performance of screwed single-lap CFRPI–TC4 joints. Based on experimental results, the effect of high temperature on joint strength and stiffness and the repair efficiency of insert are analyzed and discussed. Moreover, a new analytical model is established to evaluate the joint stiffness at RT and high temperature. Following conclusions can be drawn from the study.

Joint strength and stiffness for all configurations are lower at 250℃ than that at RT, showing the expected detrimental effect of high temperature on joint strength and stiffness. The reductions in joint strength and stiffness depend on the joint configuration.

The repair efficiencies of embedded conical nut for joint strengths of protruding and countersunk head screw joints decrease, but those for joint stiffness increase at 250℃ as against at RT. Unlike the repair efficiencies of embedded conical nut, the repair efficiency of bushing for joint strength is slightly greater, but that for joint stiffness is less at 250℃ than at RT.

The developed analytical model is capable of predicting the displacement of screwed single-lap CFRPI–TC4 joints at RT and high temperature, and there is good agreement between the experimental data and the predicted curves.

The predicted results from the proposed model show that the increase in plate length decreases joint stiffness, whereas the increases in the plate thickness and the ratio of width to diameter increases joint stiffness. The increase in the shank-hole clearance of composite plate has negligible impact on join stiffness, but significantly increases the slip displacement in stage II. Both screw tightening torque and friction coefficient of assembly surface have significant influence on joint stiffness and load–displacement curve.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project was supported by the National Natural Science Foundation of China (Grant No. 51875021).

ORCID iD

Jun-Jiang Xiong

Notation

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