Notched tensile response and damage mechanism of the GLARE laminate

Abstract

Glass laminate aluminum reinforced epoxy, as an attractive material for advanced aerospace applications, is most likely to face the challenge of various blunt notched damages. In this paper, the tensile tests of the glass laminate aluminum reinforced epoxy with circular and square blunt notches are conducted. The effects of notch geometry, such as notch diameter, notch corner radius, and off-axis angle, on the laminated tensile behaviors of glass laminate aluminum reinforced epoxy laminate are explored. A characteristic distance function representing the damage-affected region of notch is empirically constructed to predict the residual strength of the circular notched glass laminate aluminum reinforced epoxy based on a modified point stress criterion. For the square notched laminate, the strength is almost equal to that of the laminate with its circumscribed circle notch. Furthermore, the variation of two fracture patterns observed with the notch geometry is studied, and the evolution of the interlaminar delamination damage is analyzed after the metal chemical removal.

Keywords

Glass laminate aluminum reinforced epoxy tensile response residual strength damage mechanism

Introduction

Fiber metal laminates (FMLs) are the adhesively bonded hybrid materials consisting of thin metal sheets and fiber-reinforced polymer layers. A typical example of FMLs is a S2 glass laminate aluminum reinforced epoxy (trade name GLARE) invented by Delft University.¹ The fiber bridging action of the GLARE laminate can effectively retard or even arrest the crack growth in the metal layer.^2–7 It has been widely employed in the aerospace structures due to its several advantages, such as excellent fatigue and impact resistance, high specific static properties, flame resistance, and ease of manufacture.^8–13 The aircraft structure contains many inevitable fastening open-holes, such as the skin, windows, doors, and necessary inspection holes, resulting in the weakening of the mechanical property.^14–17 The blunt notch strength is an important design parameter, which is defined as the strength of a structure containing an open hole.¹⁸

Recently, most researches focus on the effects of different geometric characteristics, loading types, and fiber stacking sequence on the notch strength and damage behavior of the GLARE laminate. Abhishek et al.¹⁹ studied the mechanical properties of the GLARE with different fiber orientations (0°–60°), which shows a significant effect on the tensile and flexural strengths. Law et al.²⁰ investigated the tensile behaviors of CFRML, ARALL, and GLARE with saw-cuts and circular notch holes. It was found out that the strength reduction of saw-cut specimens is more obvious than that of the circular hole ones. A stable crack growth is observed in each layer of the saw-cut specimens, but unavailable in aluminum layers of the circular hole ones. De Vries et al.²¹ carried out the uniaxially tensile tests of GLARE variants with blunt open hole. There appears a larger difference in the strength reduction in the L and T directions. Whitney and Nuismer^22,23 presented two stress fracture criteria, the point stress criterion (PSC) and the average stress criterion, to predict the notched tensile strength of fiber-reinforced composites. Roebroeks²⁴ proposed a model based on the Norris interactive failure criterion and MVF approach, which could well predict the notch strength of FMLs under arbitrary in-plane loading conditions, including the off-axis loading. However, there are few studies on the notch shape sensitivity and damage failure mechanism of GLARE laminates with blunt notches, especially for square open-hole.

In this paper, the tensile property and damage mechanism of the GLARE laminate with circular and square notches are studied, exploring the effects of geometric characteristics of blunt notch, such as notch shape, notch size, and off-axis angle. The residual strength of the GLARE with the circular notch is predicted by a modified PSC model. Considering corner radius variation of square notch and damage affected zone of circular notch, the strength relationship between the circular- and the square-notched laminate is constructed. The chemical etching method is employed to find out the interlaminar damage evolution process. All the above researches can provide more effective guidance for the design and optimization of the GLARE structure, meeting the demands of structural applications of the aerospace and other industries.

Residual strength prediction

According to the point stress criterion (PSC),^22,23 the residual strength of composite laminate can be depicted based on the stress distribution adjacent to the circular notch. It is assumed that when the distance from the hole is d₀, the normal stress, $σ_{y}$ , reaches the failure strength of the unnotched plane

σ_{y} (x, 0) = σ_{0} at x = r + d_{0}

(1)

where r is the radius of the circular hole. The characteristic distance, d₀, represents the damage affected zone,²⁵ which is determined from the experimental data.

For an infinite orthotropic plate subjected to a uniform stress, $σ_{y}^{\infty}$ , along the y-axis, the normal stress, $σ_{y}$ , in x-axis through the hole can be expressed as²⁶

\begin{matrix} σ_{y} (x, 0) = (\frac{σ_{y}^{\infty}}{2}) (2 + (\frac{r}{x})^{2} + 3 (\frac{r}{x})^{4} - (K_{T}^{\infty} - 3) \\ \times [(5 (\frac{r}{x})^{6} - 7 (\frac{r}{x})^{8})]), x > r \end{matrix}

(2)

where

K_{T}^{\infty}

is the stress concentration factor for an infinite orthotropic plate with a circular hole, which can be calculated from the orthotropic elastic properties of the plate as follows

K_{T}^{\infty} = 1 + \sqrt{2 (\sqrt{E_{yy} / E_{xx}} - ν_{yx}) + (E_{y} / G_{yx})}

(3)

where

E_{yy}

E_{xx}

G_{yx}

, and

ν_{yx}

are the axial, transverse, shear modulus, and Poisson’s ratio of the laminate, respectively. The normalized residual strength is derived as

\frac{σ_{N}^{\infty}}{σ_{0}} = \frac{2}{2 + η^{- 2} + 3 η^{- 4} - (K_{T}^{\infty} - 3) (5 η^{- 6} - 7 η^{- 8})}

(4)

where

η = (r + d_{0}) / r

is the ratio of the damage-affected zone of the blunt notch.

σ_{0}

is the unnotched tensile strength of the plate. The notch strength of the finite width plate,

σ_{N}

, can be also expressed as

σ_{N} = σ_{N}^{\infty} \cdot \frac{K_{T}^{\infty}}{K_{T}}

(5)

where the normalized finite width correction factor,

\frac{K_{T}^{\infty}}{K_{T}}

, is given as²⁷

\frac{K_{T}^{\infty}}{K_{T}} = \frac{3 (1 - β)}{2 + (1 - β)^{3}} + \frac{1}{2} (β M)^{6} (K_{T}^{\infty} - 3) [1 - (β M)^{2}]

(6)

where the notch rate of the specimen, β, is defined as

β = 2 r / W

(7)

M^{2} = \frac{\sqrt{1 - 8 [(3 (1 - β)) / (2 + (1 - β)^{3}) - 1]} - 1}{2 β^{2}}

(8)

However, the characteristic distance, d₀, is related to the material, stacking sequence, and the notch geometry.^28,29 It can be empirically depicted as³⁰

d_{0} = k^{- 1} β^{m}

(9)

where k is the notch sensitivity factor, and m is the empirical power exponent.

Preparation and experimental procedure

The GLARE 3-3/2-0.5 is prepared by alternating layer of 2024-T3 aluminum alloy sheets and S-glass fiber/epoxy prepregs, whose properties are listed in Table 1. The detailed preparation flow of the laminate is shown in Figure 1. To obtain a stronger interfacial bonding, surface pretreatment is performed on the aluminum sheets, followed by spraying of the adhesive solution before the laminated layer. A hot-press molding process is employed subjected to a curing temperature of 120℃ and pressure of 0.5 MPa for 2 h.

Table 1.

Mechanical properties of parent materials of GLARE.

Material	E₁ (GPa)	E₂ (GPa)	G₁₂ (GPa)	υ ₁₂	t (mm)
2024-T3	72	–	27	0.33	0.5
S-glass fiber	48.8	14.3	5.1	0.29	0.125

The quasi-static tensile tests are performed according to the ASTM D-3039 standard³¹ with a loading rate of 1 mm/min. Two geometries of the laminate with an open hole are shown in Figure 2(a), where circular and square notches are located in the center of the specimens. Five hole diameters (D = 2 mm, 4 mm, 6 mm, 8 mm, and 10 mm) are chosen for the circular notch. The characteristic dimension of the square notch is set as 5 mm. Moreover, four off-axis angles (θ = 0°, 15°, 30°, and 45°) and five corner radius (R = 0.5 mm, 1 mm, 1.5 mm, 2 mm, and 2.5 mm) are designed in Figure 2(b). When the corner radius is 2.5 mm, the square notch becomes its inscribed circle notch. All test dimensions of specimens are actually measured and averaged.

Results and discussion

Tensile property of the unnotched GLARE

As shown in Figure 3, the tensile stress–strain curves of unnotched specimens show a good agreement. It indicates that the present process of the GLARE is very stable, and the potential of parent material is fully released. As the load increases, the role of fiber bridging becomes more obvious. The load-bearing pattern varies from high-modulus metal-dominated to high-strength fiber-dominated, which results in a bilinear trend followed by a complete fracture. Slight fluctuations occasionally appear in the latter linear region, which may be caused by random inherent defects, such as fiber damage, fiber buckling or knotting, or resin matrix pores. These can induce some slight cracking sound during the test.

Tensile property of the GLARE with circular notch

Figure 4 shows the stress–strain curves of the GLARE with circular notch of 0 mm to 10 mm diameter, similarly displaying a bilinear trend. The notch weakens the effective cross-sectional area for load carrying and results in stress concentration, which would accelerate the fracture of the specimen. The bigger the diameter of the circular notch, the lower the residual strength of the laminate. Simultaneously, the increasing notch gradually suppresses the potential of the parent material, especially for the fiber bridging action. Therefore, the bilinear pattern of the tensile curve tends to the linear one. Compared with the unnotched laminate, the notch strength approximately decreases by 47% for the maximum notch rate (0.4) in the present research, as well reduces by 20% for the minimum notch rate (0.08). The tensile modulus and ultimate strength of the GLARE both broadly show a linear decrease with the increasing of the circular notch rate, as shown in Figure 5. An obvious reduction of the ultimate strength and tensile strain implies that the tensile property of the GLARE laminate is very sensitive to an open hole. However, the sensitivity becomes weakening as the notch size increases.

For circular notched specimens, the characteristic distance, d₀, is determined from equation (4). The effects of notch rate on the residual strength and characteristic distance are displayed in Figure 6. The characteristic distance gradually enlarges with notch rate increases. The expanding damage-affected zone leads to an obvious decrease of the normalized residual strength. An empirical power function model, which defines the relationship between characteristic distance and notch rate, is fit in Figure 6 as equation (9). It has a very small error in the range from 1.3% to 3.7%. Therefore, the model can credibly be used to predict the actual residual strength of the GLARE with various circular notches. As listed in Table 2, the predicted strength based on the modified PSC model has an excellent agreement with the experimental results. The relative error is less than 3%.

Table 2.

Comparison between the experimental and the predicted value of circular notched strength.

β	Test σ_N (MPa)	Modified PSC
β	Test σ_N (MPa)	σ_N (MPa)	Relative error (%)
0.0800	360.27	359.96	−0.08
0.1602	328.69	320.40	−2.5
0.2406	296.63	289.33	−2.5
0.3204	262.5	260.27	−0.9
0.3997	237.74	231.95	−2.9

PSC: point stress criterion.

The blunt notch would generally activate a bigger damage affected or stress concentration zone than the notch zone. It can also be roughly represented by characteristic distance, d₀, along the T-direction. Thus, only taking the notch diameter into consideration, the net stress, σ_net, inevitably deviates from the actual value. As shown in Figure 7, the stress ratio of the blunt notch, σ_N/σ_net, is decreasing as the notch ratio increases. This indicates that the bigger notch ratio plays a more negative role in the residual strength of the GLARE. The increasing notch diameter could weaken the stress concentration, which suppresses the outward expansion of the damage-affected zone to some extent. Therefore, the reduction of the damage-affected zone ratio of blunt notch, η, slows down as the notch ratio increases.

Tensile property of the GLARE with square notch

According to application requirements, the square notch of the GLARE laminate is likely designed as the round-corner pattern, ever with the off-axis angle. It can effectively relieve high stress concentration induced by sharp corner and be convenient for processing and assembly. As shown in Figure 8, the effect of the corner radius on the residual strength of the GLARE is displayed at different off-axis angles. An increase in the corner radius decreases notch damage and stress concentration, resulting in a strength improvement. When the square notch transforms into a circular one (R = 2.5 mm), the notch strength rapidly increases by an average of 10%. Moreover, the variation of the off-axis angle of notch hardly has an influence on the above trends. However, a strength degradation occurs with the increase in the off-axis angle, which becomes more serious as the corner radius decreases. Note that inversely a great strength promotion appears at 45° off-axis angle due to the failure mode transition of the GLARE. When the angle is within 45°, diagonal shear failure generally is dominated due to high stress at corners of the square notch. But the tensile fracture failure is activated when the square diagonal is perpendicular to the loading direction. It is more beneficial to fully release fiber’s mechanical potential.

The effects of the corner radius on the modulus and the fracture strain of the GLARE laminate both show a similar trend, as shown in Figures 9 and 10 respectively. The modulus has also shows a slowed rise with the increasing corner radius, followed by about 15% rapid growth at R = 2.5 mm. Similarly, those above mentioned are independent of the off-axis angle of the square notch. As opposed to the notch strength variation, the modulus slightly enhances as the off-axis angle increases. Moreover, the increasing off-axis angle results in a decelerating descent of the fracture strain of the notched GLARE, and an increasing strain difference caused by the corner radius.

All results above-mentioned suggest that with the same geometric characteristic length of blunt notch, the tensile property of the square notched GLARE is significantly weaker than that of the circular notched one. For square notch specimens, the variation trend of tensile property with notched corner radius hardly depends on the off-axis angle of notch. Inversely, the corner radius has a non-negligible effect on the notched property variation with off-axis angle. As shown in Figure 11, compared with the equal-area circular and equivalent effect circle, the notched strength with circumscribed circle of square shows a better agreement with that of the square for various corner radiuses. All deviations are within 2%. Equal-area circle is the same area as the square notch, and equivalent effect circle is the circle including damage characteristic distance, d₀, based on the inscribed circle of the square notch. Therefore, the square notch strength of the GLARE can be equivalent to a circular notch one with the circumscribed notch of square, which can be also predicted based on the modified PSC model. The above result suggests that the high stress concentration caused by the geometrical corner of the square notch is the predominant reason for strength degradation, rather than the loss of the cross-sectional area.

Damage mechanism of the notched GLARE

The geometric changes of blunt notch generate two main failure patterns, tensile fracture and diagonal shear fracture. Simultaneously, multiple hybrid failure modes may occur as shown in Figure 12. For the specimens with circular notch, a flat tensile fracture emerges, accompanied by the local fiber pull-out and matrix cracking, as well as the square notched one with 45° off-axis angle. However, the former fracture displays a more obvious ductile characteristics and necking phenomenon of aluminum layer, as observed in Figure 12(a). High stress at the corner of square notch accelerates the crack initiation and propagation in aluminum layer, and the plastic behavior is not fully developed for the latter. The square specimens without off-axis angle show a typical ragged shear fracture, accompanied by the local delamination, fiber breakage, and pull-out, as shown in Figure 12(b). The metal crack initiates at the corner of square notch, forming the zigzag diagonal fracture. The rotation of the square notch conducts the failure mode change from tensile fracture to shear fracture, exactly as shown in Figure 12(b) and (c).

The blunt notch can arouse the local damage, which gradually propagates under the applied load. The failure mechanism of the GLARE also has some attractive variations with the notch geometry, as illustrated in Figure 13. The more interlaminar damage can be clearly observed by chemical removal of aluminum layer at the outer surface of the GLARE. The circular notch tends to an elliptical hole under tensile loading, followed by obvious crack-tip opening like type-I blunt crack. The mouth opening is degraded as the notch diameter increases. For the square notched GLARE, the initial crack originates from the edge of transition corner, leading to a shear fracture like mixed-mode crack of type-I and type-II. The increasing corner radius and off-axis angle both weaken the shear failure, even completely activate the tensile fracture when the R = 2.5 mm or θ = 45°. A couple symmetrical triangle delamination region appears for the circular notched GLARE, and a diagonally symmetric triangle region for the deflective square notched one. The square notched GLARE without off-axis angle displays a couple symmetrical trapezoid delamination region. However, the crack propagation induced by high stress corner of off-axis notch along T-direction suppresses the occurrence of delamination damage to some extent.

According to all-above illustrated contours, the ultimate damage wide is measured as show in Figure 14. For the circular notched GLARE, the delamination damage region gradually degrades as the notch diameter increases. However, due to the change in the initial crack position, for the square notched GLARE, the delamination damage region expands with the increasing corner radius of the square notch with the off-axis angle, and inversely for the square one without the off-axis angle.

Conclusions

The tensile behaviors of GLARE 3-3/2 laminates with circular and square blunt notches are studied in the present paper. The responses of mechanical property and damage mechanism on notch geometry are explored, including the sharp, size, and rotation of the blunt notch. For the circular notched GLARE, the residual strength shows a linear decline after a sharp drop as the notch rate increases, as well as an approximately linear decrease for the modulus. A tensile fracture emerges, and the damage region of interlaminar delamination reduces with the increasing notch diameter. For the square notched GLARE, the variation trends of tensile properties with corner radius hardly depend on the off-axis angle. A diagonal shear fracture tends to become tensile fracture with the off-axis angle increases of the square notch. With the increase in the corner radius of square notch, the delamination damage region tends to expanding. Furthermore, a modified PSC model, based on the characteristic distance of the notch damage affected region, can accurately predict the residual strength of the circular notched GLARE. And the square notched strength can be effectively substituted by the laminate strength with circumscribed notch of square.

Footnotes

Declaration of Conflicting Interests

The author(s) declared following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: All authors declare that: (i) no support, financial or otherwise, has been received from any organization that may have an interest in the submitted work; and (ii) there are no other relationships or activities that could appear to have influenced the submitted work. We confirm that this article has not been previously published in any format, is not under consideration for publication elsewhere, and that the publication has been fully approved by all stakeholders.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (No. 11502031, No. 51874043, No. 51701021), Capital Construction Project within the Provincial Budget 2019 of Jilin Province Development and Reform Commission of China (No. 2019C046-6), and Science and Technology Research Project of Education Department of Jilin Province of China (No. JJKH20181029KJ).

ORCID iD

Liang Gao

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