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Archives of Civil and Mechanical Engineering (2020) 20:39 https://doi.org/10.1007/s43452-020-00025-1

ORIGINAL ARTICLE

Delamination analysis in single‑point incremental forming of steel/steel bi‑layer sheet metal

M. Hassan1 · G. Hussain1 · M. Ilyas1 · A. Ali1

Received: 28 June 2019 / Accepted: 22 December 2019 © Wroclaw University of Science and Technology 2020

AbstractLayered metallic materials (LMMs) offer superior properties in comparison to their counterpart monolithic sheets. Single-point incremental forming (SPIF) has emerged as an economical solution to produce LMM parts. However, delamination can limit the formability of such parts. In this study, the delamination analysis during SPIF of layered sheets was performed. Steel/steel bi-layer sheets were fabricated by roll bonding. These sheets were produced at thickness reduction ratios of 47%, 58% and 70%. The bond strength and fracture toughness in mode I and mode II were determined by T-peel and tensile shear tests, respectively. When the thickness reduction ratio was increased from 47 to 70%, an increase in bond strength was observed with 572% increase in mode I and 15.6% in mode II, respectively. On the other hand, with the same percent increase in thickness reduction, the critical strain energy release showed an increase of 3992% in mode I and 20% decrease in mode II. Surface-based cohesive zone model was used to define the interface between layers during numerical simulation of SPIF for delamination analysis. To validate the numerical results, SPIF of given bi-layer sheet was performed experimentally and a good agreement between the numerical and experimental results was observed.

Keywords Layered metallic materials (LMMs) · Single-point incremental forming (SPIF) · Formability · Delamination

1 Introduction

In recent past, notable progress in the development of lay-ered metallic materials (LMMs) for numerous applications has been witnessed. LMMs can be manufactured by various processes including explosive welding, diffusion welding, roll bonding, and laser bonding. However, roll bonding is considered more efficient and cost-effective in comparison to other processes as reported by Wong et al. [1]. Also, no filler or adhesive agent is required in roll bonding. Roll bonding is a type of welding process in which a stack of similar or dissimilar metals is passed through rollers to promote a good bond between the metallic sheets at the cost of reduction in thickness. Yin et al. [2] recognized hot roll bonding as the most effective method to fabricate layered materials.

In forming of LMMs, the most reasonable method in term of tooling cost and lead time is single-point incremental

forming (SPIF) as reported by K. A. Al-Ghamdi and Hus-sain [3]. SPIF is a rapid prototyping method and is most appropriate for small batch production. SPIF has shown its suitability to produce 3D parts, which can be complex in nature, without utilizing dedicated die and with low-energy demand as described by Gupta and Jeswiet [4]. The advan-tages of SPIF technology are its adaptability, higher form-ability, shorter prototyping time and inexpensive die/tooling in comparison to the conventional sheet forming technolo-gies. The most common performance indicator in SPIF is formability, which is the limiting wall angle of sheet without failure.

There is noteworthy research being carried out in the field of SPIF in the ongoing years, because of its numer-ous advantages. Extensive research has been done on the deformation mechanism and fracture behavior of mono-lithic sheets in SPIF. However, limited efforts have been spent on the SPIF of layered metallic sheets. Al-Ghamdi and Hussain [3] examined the formability of the Cu/Steel clad sheet in SPIF process experimentally and found that failure in clad sheet occurred in same manner as in the mon-olithic sheet. In another work, Al-Ghamdi and Hussain [5] explored experimentally the impact of process parameters on

* G. Hussain ghulam.hussain@giki.edu.pk; gh_ghumman@hotmail.com

1 Faculty of Mechanical Engineering, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, Topi, Pakistan

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the formability of Cu–Steel–Cu clad sheet in SPIF process. Al-Ghamdi and Hussain [6] compared SPIF and stamping processes formability for clad of Cu/St prepared through roll bonding. The study revealed that similar to the mono-lithic sheet, incremental forming also enhanced the form-ability of the clad sheet. Gheysarian and Honarpisheh [7] explored the layer arrangement in SPIF of Al/Cu bimetal prepared through explosive welding technique. The impor-tant finding of this research regarding layer arrangement is that the material having low yield strength shall be used as the inner layer. Sakhtemanian et al. [8] investigated the deformation behavior of low carbon steel/commercial pure titanium bi-layer sheet in the incremental forming process. In finite element (FE) simulations, they used tie constraint between the two sheets to simulate SPIF. However, using tie constraint between the two sheets, it is not possible to predict the delamination failure. Ashouri and Shahrajabian [9] examined the formability of brass/St13 clad in SPIF in terms of fracture height and fracture angle. The results dis-closed that increase in vertical step size, tool diameter and feed rate have a negative effect on the formability of Brass/St13 clad. Till date, there has been no significant work done to analyze the delamination behavior of bi-layer sheet in the incremental forming process.

In this work, delamination analysis of steel/steel (St/St) bi-layer sheets has been performed. For this purpose, the St/St bi-layer sheet has been prepared by roll bonding technique at varying thickness reduction ratios of 47%, 58% and 70%, at a constant pre-rolling temperature of 950 °C. It has been found that layers joining occur if reduction ratio of at least 47% is applied. Below 47% reduction, no bond was formed between two sheets. The effects of varying thickness reduc-tion ratio on the bond strength, critical strain energy release rate and formability of SPIF have been evaluated. The delamination analysis has been performed for samples man-ufactured at 47% thickness reduction ratio and pre-rolling temperature of 950 °C. This thickness reduction is selected for delamination analysis as St/St bi-layer sheet has mini-mum bond strength at this thickness reduction and is more susceptible to delamination. To speculate the delamination behavior in SPIF of St/St bi-layer sheet numerically, surface-based cohesive zone model (SCZM) has been used to define the interface between two sheets. To validate the numerical results, experimental tests have also been conducted.

The methodology for the present investigation is briefly explained for better understanding of this article. First of all, the interface of St/St bi-layer was characterized experimentally both in mode I and II using T-peel and tensile shear tests, respectively. These results were then used to formulate the interface model between the layers numerically. This interface model was used in a 3D FE model to simulate the SPIF process for St/St bi-layer sheet having a thickness reduction of 47% and

perform delamination analysis. SPIF experiments were then conducted to validate the numerical results.

2 Specimen preparation

The material used for the SPIF of St/St bi-layer sheet was deep drawing quality steel DC03 with no alloying elements other than carbon (0.1%) and iron (99.9%). For a good bond between the two sheets, layers of contaminants from the surfaces of sheets to be joined were removed by chemical and mechanical cleaning which are the two most commonly used methods to remove any barrier to bonding. Before passing St/St bi-layer sheets through rollers, the leading and trailing edges of the two sheets were spot welded to avoid the misalignments of two sheets. Roll bonding was carried out to produce three different reduction ratios, i.e., 47%, 58%, and 70%. Before roll bonding, specimens were heated in a box furnace at 950 °C.

3 Interface characterization of bi‑layer sheet

3.1 T‑peel test

The interface properties of the bi-layer sheet in mode I loading were measured by the T-peel test according to the ASTM-D1876 standard [10]. The peel tests were conducted using a Universal Testing Machine (INSTRON-5567) with a 30 kN load cell. The dimensions and schematic illustration for the T-peel test are portrayed in Fig. 1. Further details are already presented by the authors in [11].

3.2 Tensile shear test

The tensile shear test was performed to measure the interfa-cial properties of bi-layer sheet under shear load (mode II/III). The test procedures were followed according to ASTM D1002 standard [12]. The dimensions of the sample are shown in Fig. 2. The average bond strength ( �c ) was determined using Eq. (1) [13]:

The interfacial fracture toughness terms of critical strain energy release rate was measured using the relation (2) [14]:

where Pc is load at crack initiation, �c1 is the displacement corresponding to damage initiation, �c2 is the displacement at the end of plastic plateau region and �f corresponds to failure displacement.

(1)�c =Pc/Aoverlap

.

(2)GIIc =1

2�max

[�c1 + 2

(�c2 − �c1

)+(�f − �c2

)],

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3.3 Results and discussion for experimental interface characterization

The influence of thickness reduction on the force–displace-ment plot of St/St bi-layer sheet in mode I and II is depicted in Figs. 3 and 4, respectively. In mode I, the bond strength increases from 2.127 ± 0.17N∕mm at thickness reduction of 47% to 14.3 ± 0.4 N/mm at thickness reduction of 70% as shown in Fig. 5a. The increase in bond strength with the enhancement of thickness reduction is 572%. As can be seen from Fig. 5b, the bond strength depicts a similar trend in

mode II as observed in mode I. In mode II, the bond strength increases from 4.5 ± 0.08 N/mm2 at thickness reduction of 47% to 5.2 ± 0.02 N/mm2 at thickness reduction of 70%, i.e., increase of 15.6%. Figure 6a shows the enhancement of fracture toughness in terms of critical strain energy release rate for mode I with an increase in thickness reduction, i.e., from 101.4 ± 3.64 J/m2 at thickness reduction of 47% to 4150 ± 164 J/m2 at 70% thickness reduction. However, the fracture toughness for mode II shows a decreasing trend for an increase in thickness reduction with values ranging from 2500 J/m2 at 47% to 2000 J/m2 at 70% as depicted in Fig. 6b.

Fig. 1 a Dimensions of T-peel sample in millimeter; b a schematic representation for the T-peel test

Fig. 2 A schematic representa-tion of the tensile shear test sample

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Moreover, it is clear from the optical micrographs that at high thickness reduction, a good bond between the two steel sheets was formed while at low thickness reduction, an unbonded region also existed between the two sheets as shown in Fig. 7. Thus, a large amount of force was required to separate the two sheets bonded at high thickness reduc-tion, resulting in high bond strength. Hosseini and Danesh Manesh [15] have shown that bond strength improves with increase in thickness reduction, because area of the cracks and the volume of the virgin metals to be extruded through the cracks increased leading to high bond strength. Mova-hedi et al. [16] has shown that with increase in thickness reduction ratio and rolling pressure, surface expansion and micro-cracks formation increases result in large bonded area. Jing et al. [17] has also indicated the same kind of effect

of rolling thickness reduction on bond quality. Monazzah et al. [18] found that micro-cracks available on surfaces to be bonded together facilitate the bonding process. The study further revealed that fracture toughness, bond strength and rolling thickness reduction have a direct relation. In another study, Monazzah et al. [19] explored that delamination of bonded sheets are a phenomenon similar to initiation and propagation of crack. The enhancement of bonding strength by increasing the rolling strain postpones the initiation of delamination.

4 Numerical modeling of interface

St/St bi-layer sheet having thickness reduction of 47% had the least bond strength in both modes I and II. Therefore, numerical simulation for delamination analysis was per-formed only for this thickness reduction due to its high susceptibility for delamination. The interface between two sheets was modeled using surface-based cohesive zone model (SCZM).

4.1 Mode I simulation

The values of penalty stiffness, limiting stress and fracture toughness in the normal direction (mode I) were determined from T-peel test. The details are presented and discussed by the authors in [11]. Table 1 shows the final values of limiting stress ( �nn ) and penalty stiffness ( Knn ) in mode I.

4.2 Mode II simulation

The interface parameters in mode II were determined from the tensile shear test. Limiting interface strength and penalty stiffness were determined experimentally. It is clear from the experimental results that St/St bi-layer sheet follows a trap-ezoidal cohesive traction–separation law as shown in Fig. 8.

In numerical modeling, damage evolution for trapezoidal traction separation law was defined in terms of damage vari-able D and effective displacement. Based on effective sepa-ration, D is defined for trapezoidal traction separation law as:

where �c1 , �c2 and �f are the displacements at damage initia-tion, end of plastic plateau region and failure, respectively. The contact status for mode II delamination test is shown in Fig. 9.

The comparison of experimental and numerical results is depicted in Fig. 10. In mesh convergence analysis, it was

(3)D =

⎧⎪⎨⎪⎩

1 −�c1

�Plateau region

1 −�c1(�f−�)�(�f−�c2)

Softening region,

Fig. 3 Peel force versus displacement plot for mode I

Fig. 4 Force–displacement plot for mode II

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found that the mode II delamination test was mesh independ-ent as shown in Fig. 11.

The interface parameters for mode II are shown in Table 2.

For mode III, the same interface parameters were used as in mode II.

5 Simulation of SPIF

After determination of interface parameters for both modes I and II, a 3D FE model was constructed to simulate the SPIF process and perform delamination analysis. The sheets and tool were modeled as deformable and analytical rigid bodies,

respectively. A blank size of 100mm diameter and a hemi-spherical tool with 10 mm diameter were considered. The nature of the plate material was considered as elastoplastic with isotropic hardening behavior. The elastic properties of steel are shown in Table 3. The plastic behavior was given in terms of true stress–strain data determined by perform-ing tensile test as shown in [11]. The tool trajectory during SPIF was defined in x-, y-, and z-directions. The feed rate of 1300 mm/min and a step depth of 0.4 mm were provided with no rotation. The designed depth was 20 mm. The vary-ing wall angle cone (VWAC) was used as test geometry. The final deformed part had a major diameter of 48 mm and the minor diameter of 25 mm with varying wall angle of 30–90°. The simulation was performed as dynamic explicit analysis.

Fig. 5 Variation in average bond strength of St/St bi-layer sheet versus thickness reduction a mode I, b mode II

Fig. 6 Variation in fracture toughness of St/St bi-layer sheet versus thickness reduction a mode I, b mode II

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Tool trajectory to be followed is depicted in Fig. 12. Details of different boundary conditions specified on both the tool and the work piece are presented in Fig. 13. The numerical model of St/St bi-layer sheet for SPIF simulation is shown in Fig. 14. To model the interface between the two sheets,

surface-based cohesive interaction was used. To check whether the failure mode is mode I, II, III or mixed mode, the simulation of SPIF was performed by considering only the penalty stiffness values in mode I, II and III and without incorporating any damage law. It was found that the nodes at the interface only slide relative to each other during SPIF without separation in normal direction. Thus, the failure mode that will cause delamination of the given bi-layer sheet is shear mode (mode II/III). Therefore, for damage evolu-tion, only pure sliding mode was considered. The damage evolution for sliding mode was defined in terms of damage variable D and effective displacement.

To reduce the computational time, mass scaling was used. In this technique, the mass of an element of the mesh increases artificially in term of material density to increase the time increment value [20]. The advantage of this tech-nique is that it does not affect the rate dependence of the material [21]. However, for dynamic study, it is essential to check the effect of ‘‘nonphysical’’ mass on results. A common technique to check mass scaling effect is that if the ratio of kinetic and the internal energy of the system is below 5–10%, the mass scaling does not affect the results [22]. Figure 15 depicts the comparison of effect of different mass scaling factors on St/St bi-layer sheet. It is clear that in all the cases, the ratio of kinetic and internal energy of the St/St bi-layer sheet is below 10%. However, it can be seen that at high mass scaling factor of 1 × 108 and 1 × 106 , an instabil-ity arises when the tool touches the sheet initially. At mass scaling factor of 1 × 105 no instability arises. Thus, mass

Fig. 7 Micrographs for St/St bi-layer sheet a 70% thickness reduction b 58% thickness reduction c 47% thickness reduction

Table 1 Limiting stress ( �nn

) and penalty stiffness ( K

nn ) for

interface in mode I

�nn

[ MPa] 1.4Knn

[N/m3] 6.5 × 1010

Fig. 8 Traction separation law for in-plane shear mode

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scaling factor of 1 × 105 was selected to perform numerical simulation for SPIF of St/St bi-layer sheet.

5.1 Delamination analysis in St/St bi‑layer sheet

The delamination failure in St/St bi-layer sheet was predicted numerically in terms of scalar stiffness degradation for cohesive surfaces (CSDMG). When the value of CSDMG becomes equal to 1, it indicates the damage of the cohesive interface is completed and delamination occurs. The delami-nation behavior of St/St bi-layer sheet having a thickness reduction of 47% formed through SPIF is shown in Fig. 16 using different mesh sizes.

The effect of various mesh sizes on delamination depth is shown in Table 4. It was numerically found that the SPIF model became mesh independent at an element size of 1 mm. The delamination occurs at a depth of 8.4 mm. To validate the model, experimental tests were then performed.

6 SPIF experiments

Three-axis CNC machine (TRIAC FANUC) was used to form the part in SPIF. The circular blank of 100 mm diameter and high-speed steel (HSS) forming tool having 10 mm diameter was used. The feed rate of 1300 mm/min

Fig. 9 Interface contact status for mode II delamination test

Fig. 10 Comparison between experimental and numerical results for mode II delamination test

Fig. 11 Effect of mesh size on force–displacement curves for mode II delamination test

Table 2 Limiting stress ( �ss)

and penalty stiffness ( Kss

) for interface in mode II

�ss

[ MPa] 4.75Kss

[N/m3] 1.7 × 1010

Table 3 Material properties for blank

Material Young’s modulus [GPa]

Poisson’s ratio Density [kg/m3]

Steel (DC03) 210 0.3 7850

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and a step depth of 0.4 mm were provided with no spindle rotation. To reduce the friction between forming tool and blank, mineral oil was used. The SPIF experimental setup

is shown in Fig. 17. The varying wall angle cone (VWAC) was used as test geometry. The radius of generatrix was 23.09 mm as shown in Fig. 20. The 3D CAD model of the

Fig. 12 Tool trajectory for varying wall angle cone (VWAC)

Fig. 13 Boundary conditions specified during numerical simulation of SPIF

Fig. 14 Numerical model for SPIF simulation

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part was developed in Creo Parametric and NC (numeri-cal control) codes were generated. These codes were then transferred to the CNC machine tool to form the part of the desired shape.

The depth at through thickness bulk fracture ( hf) was measured using dial gauge and the formability in term of maximum wall angle was measured from Eq. (7) derived by Hussain et al. [23] using the principal scheme shown in Fig. 18.

If the point on the curve at which fracture occurs is represented by Pf

(yf, zf

) and hf is the depth of part at the

occurrence of failure, the limit wall angle ( �max ) can be calculated using Eq. (4) [24]:

where R represents the radius of generatrix.

(4)�max = �f = cos−1(yfR

)= cos−1

(y1 − hf

R

),

6.1 Experimental results of SPIF

During SPIF of St/St bi-layer sheet formed at variable wall angle, it was found that the bulk material failed at a depth of 7 mm. Upon investigation of the specimens, no delamination was observed up to this depth as shown in Fig. 19.

7 Comparison between experimental and numerical results for SPIF of bi‑layer sheet

From the numerical simulations, it was predicted that delamination in St/St bi-layer sheet occurs at a depth of 8.4 mm. From the experimental results, it was found that the mode of failure occurs in St/St bi-layer sheet having

Fig. 15 Effect of mass scaling on St/St bi-layer sheet

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47% is bulk material fracture (through thickness fracture) at depth of 7 mm and no delamination was observed up to this depth. Results of numerical simulation of SPIF of the selected bi-layer sheet also showed that no delamination occurs up to the depth of 7 mm.

8 Formability analysis

The fracture pattern of St/St bi-layer sheet for various thickness reduction ratios is portrayed in Fig. 20. The

Fig. 16 Delamination analysis of St/St bi-layer sheet in SPIF at various mesh sizes

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comparison of formability is shown in Table 5. It is clear that with increase in thickness reduction ratio, form-ability of St/St bi-layer sheet in term of maximum wall angle ( �max) decreases. The decrease in wall angle with increase in thickness reduction from 47 to 70% is 8.75%. This is because, at high thickness reduction, the percent tensile area reduction (%Ar) determined by performing tensile test is low. The relationship between %Ar and form-ability at various thickness reductions is shown in Fig. 21. This is in agreement with the literature on the monolithic

Fig. 16 (continued)

Table 4 Delamination depth at various mesh sizes

Mesh size in the rectangular domain (mm) Delamination depth (mm)

2 9.21.5 8.81 8.40.85 8.40.67 8.4

Fig. 17 Experimental setup for SPIF

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Fig. 18 Principal scheme for maximum wall angle calcula-tion

Fig. 19 Failure behavior of St/St bi-layer sheet having 47% thickness reduction

Fig. 20 Fracture pattern of St/St bi-layer sheet in SPIF at differ-ent thickness reductions

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sheet [25], revealing that formability and %Ar has a direct relation with each other. Thus, it can be concluded that the formability indicator (%Ar) for the monolithic sheet is equally applicable for multilayer sheets.

9 Conclusions

In this work, delamination analysis of St/St bi-layer sheets has been performed. The following important findings are drawn from this study:

1. The formability of St/St bi-layer sheet decreases by 8.75% with the increase in thickness reduction ratio from 47 to 70%. This is because at high thickness reduc-tion, the percent tensile area reduction (%Ar) is low.

2. The bond strength in mode I and mode II increases with an increase in rolling thickness reduction. With the increase in thickness reduction from 47 to 70%, the increase in bond strength in mode I is 572% while in mode II is 15.6%.

3. With increasing rolling thickness reduction ratio from 47 to 70%, critical strain energy release shows an increase

of 3992% in mode I, while a 20% decrease was observed for mode II.

4. During SPIF of St/St bi-layer sheet at variable wall angle, the bulk material failed at a depth of 7 mm. Upon investigation of the specimens, no delamination was observed up to this depth.

5. Results of numerical simulation of SPIF of the selected bi-layer sheet also show that no delamination occurs up to the depth of 7 mm which is in agreement with experimental results. The study further predicts that delamination would initiate at a depth of 8.4 mm if the formability of the specimen was high enough to avoid bulk failure before that.

The detailed procedure presented in this study can be used as a guideline to study the delamination of bi-layer LMMs of similar or dissimilar metallic sheets.

Author contributions All authors have contributed equally in the research and writing of this manuscript.

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Forming conditions Formabil-ity ( �max)

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