Residual strength of additive manufactured ABS parts subjected to fatigue loading

Journal Pre-proofs Residual strength of additive manufactured ABS parts subjected to fatigue loading C.W. Ziemian, R.D. Ziemian PII: DOI: Reference:

S0142-1123(19)30559-6 https://doi.org/10.1016/j.ijfatigue.2019.105455 JIJF 105455

To appear in:

International Journal of Fatigue

Received Date: Revised Date: Accepted Date:

15 August 2019 16 November 2019 21 December 2019

Please cite this article as: Ziemian, C.W., Ziemian, R.D., Residual strength of additive manufactured ABS parts subjected to fatigue loading, International Journal of Fatigue (2019), doi: https://doi.org/10.1016/j.ijfatigue. 2019.105455

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© 2019 Published by Elsevier Ltd.

Residual strength of additive manufactured ABS parts subjected to fatigue loading

a

Bucknell University, Department of Mechanical Engineering, Lewisburg, PA 17837 Bucknell University, Department of Civil & Environmental Engineering, Lewisburg, PA 17837 * Corresponding author. Tel.00 1 5705771754; fax 5705777281; [email protected] b

Abstract This study investigates the effect of tension fatigue loading on the residual strength degradation of additive manufactured ABS formed by fused deposition modeling (FDM). Sinusoidal tension-tension fatigue loading with nine treatment combinations of cycling stress and duration were followed by tensile tests for 0°, +45/-45°, and +30/-60° mesostructures. Normalized residual strengths of the bidirectional mesostructures were significantly higher than that of the 0° parts for all factor combinations studied. A proposed phenomenological model, based on a strength degradation model for carbon fiber-reinforced composites, successfully described 92-96% of residual strength variability for the 0° specimens, and 77-92% for the bidirectional mesostructures tested.

Keywords Additive Manufacturing; FDM Fatigue Response; Cyclical Strength Degradation;

1. Introduction Additive manufacturing (AM) processes continue to advance from rapid prototyping methods to fabrication techniques capable of producing full-scale customized components for end use in marketable products. This trend has been fueled by the advantages offered by AM technologies, including reduced tooling costs, quicker speed to market, and the ability to produce complex component geometries. However, this advancement requires a clear understanding of the mechanical behavior of AM parts and their ability to meet expected in-service loading and operational requirements [1]. As a result, the

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literature includes a significant amount of recent work focused on the characterization of AM components and the development of models used to predict and control their mechanical properties.

Fused deposition modeling (FDM), also known as fused-filament fabrication (FFF), is a widely used AM process originally developed by Stratasys Inc. It involves the formation of thin layers by the extrusion of a partially melted flexible filament, most commonly acrylonitrile butadiene styrene (ABS) plastic, through a heated nozzle. Each FDM layer or lamina is deposited on the surface of the previous layer as the filament is extruded in a parallel pattern defined by the raster angle. As the ABS cools and bonds with adjacent filaments, the next layer is deposited. The sequence of layers and raster angles used to form an FDM component, referred to as its mesostructure, has been shown to affect the part’s anisotropic mechanical properties [2]. Although the virgin ABS is isotropic, the anisotropy is introduced by the FDM process itself, and it depends on the build orientation, the strength of the bond between layers, the angle of the fibers in a layer, and the pattern or stacking sequence of the multiple layers. A substantial amount of research has been completed to study the directional dependence of the static properties, i.e. tensile and compressive [3–10], flexural [6–8], and impact strengths [7,8], of FDM parts on different process parameters. However, there have been far fewer studies published with a focus on the dynamic mechanical properties of FDM components.

The literature has recently begun to include research results regarding the fatigue response of AM parts fabricated by FDM. The majority of this work has examined the dependence of fatigue life on different FDM process parameters. Lee and Huang [11] examined the effect of deposition angle and part-build orientation on the total strain energy absorbed during cyclical loading of FDM specimens. They tested both ABS and ABS plus. Ziemian et al. [12] studied the effect of stress level and FDM mesostructure on the uniaxial tension-fatigue life of ABS components, and found that the machine default (+45/-45°) mesostructure experienced the longest fatigue life at each normalized maximum-stress-level, followed by the 0°, 45°, and 90° specimens respectively. The differences in fatigue life were found to be statistically 2

significant at a level of a = 0.05 for all mesostructures at each stress level. Padzi et al. [13] compared the fatigue performance of ABS components formed by FDM with those fabricated by injection molding, and found the molded specimens to have higher fatigue lives for all loading levels tested. Jap et al. [14] investigated the effect of raster orientation on the fatigue life of bidirectional ABS components formed by FFF, and determined the -45°/45° specimens to achieve the longest life. Gómez-Gras et al. [15], Afrose et al [16], and Ezeh et al. [17] each examined the fatigue response of PLA parts processed by FFF. Gómez-Gras et al. [15] studied the relative influence of four process parameters on the fatigue life on PLA components, and found fill density to be the most important, followed by nozzle diameter and layer height respectively. Afrose et al. [16] analyzed the part-build orientation and found the 45° angle to result in the highest fatigue life for every stress level tested. Ezeh et al. [17] focused their investigation on the effect of raster orientations and infill percentage on the resulting S-N curves, and found raster direction to have little effect on the overall fatigue behavior of the specimens; contradicting the previously mentioned results for PLA parts. Puigoriol-Forcada et al. [18] studied the flexural fatigue properties of polycarbonate FDM specimens and determined the importance of part build orientation with regard to fatigue performance. Their work included numerical modeling and a product-based case study used for validation purposes. This sample of recent research highlights the effects of various build parameters on the fatigue life of FFF components, such as mesostructure, build orientation, layer height, and infill percentage.

This paper presents an experimental study aimed at acquiring a deeper understanding of the strength degradation that ABS-FDM parts experience when subjected to cyclical loading, and the subsequent development of an empirical residual strength model. It is difficult to find published work focused on the residual strength modeling of AM parts subjected to load cycling, however the literature is rich with cumulative damage models for fatigued composite materials. Several models are specific to fiberreinforced polymer composites and laminated polymer matrix composites [19–28], and some have been shown to achieve notable agreement with experimental results for ceramics and other brittle materials. 3

The performance of one of these models is investigated with regard to predicting the strength degradation of FDM components subjected to constant amplitude fatigue loading. Data is obtained from experimentation designed to highlight the effects of part mesostructure, cycling stress level, and fatigue life fraction on the ultimate tensile strength of pre-cycled FDM components, as well as from a previous study conducted by the authors [29]. A model from the literature, developed for carbon fiber reinforced polymer (CFRP) composites, is first tested with the data and then modified to improve its performance with regard to predicting the residual strength of FDM specimens subjected to tension-tension fatigue loading. The study provides insight into the fatigue performance of FDM parts and the associated changes in component residual strength.

2. Experimental Study 2.1 Overview Three types of physical tests were conducted in order to determine the relationship between residual strength and fatigue loading of FDM specimens, including monotonic tension tests, uniaxial tensiontension fatigue tests, and post-cycling residual strength tests. Tension tests were done originally to determine the mean ultimate tensile strength of each mesostructure studied and to explore the probability distribution associated with tensile failure. Fatigue tests were conducted using stress controlled, constant amplitude, tension-tension cycling to failure, in order to determine the mean fatigue life of each mesostructure studied. Additional specimens were then fabricated and subjected to the same stress controlled, constant amplitude, tension-tension fatigue tests, but now for a pre-determined number of cycles or fatigue life fraction. Finally, residual tensile strength tests were carried out on the pre-cycled specimens. The same material spool and process parameter settings were used for the fabrication of all specimens.

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2.2 Materials and sample preparation All testing was done using dogbone shaped specimens that were fabricated, as per ASTM D638 [30], on a Stratasys Vantage-i machine. All specimens were made of acrylonitrile butadiene styrene (ABS-P400 Stratasys®) extruded from a T12 nozzle. FDM machine process parameters were set to default or recommended values, including air gap (0.0 mm), road width (0.3048 mm), slice height (0.1778 mm), interior fill style (solid normal), and part fill style (perimeter/raster).

The specimen orientation during fabrication, shown in Fig. 1(a), was such that the minimum part dimension aligned with the outward normal of the build table (z-axis of the machine). The z-height or thickness of each specimen was 2.54 mm and was composed of 15 layers. The length along the longitudinal x-axis was 165.1 mm, and the width along the y-axis was 19.1 mm at the ends. The deposition strategy for each layer of a specimen was defined by a raster or fiber orientation angle q, measured from the +x-axis. For the residual strength study, specimens were built with three different mesostructures, or combination of fiber orientations and layering patterns. These mesostructures included one unidirectional configuration with 15 identical layers or plies, and two bidirectional laminates with 15 alternating orthogonal plies (Fig. 1(b)). The unidirectional laminates were built with a fiber orientation of q = 0º, and the bidirectional laminates were built with alternating orthogonal plies of +qº/-(q-90)º, specifically +30º/-60º and +45º/-45º.

(a)

(b)

Fig. 1. Building FDM specimens. (a) Build orientation on machine table, and (b) schematic demonstrating layering of four alternating orthogonal plies of bidirectional laminates.

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2.3 Static tension tests A thorough investigation of monotonic tensile properties was previously completed and has been published [12, 29]. An additional set of tension tests was performed in this study using sixteen specimens for each mesostructure, in order to validate previous work and explicitly test the spool of ABS material used. The ASTM D638 standard [30] was again used in testing specimens on an Instron machine with 0.057 mm displacement precision, up to 0.001 N force accuracy, and 10 kN load capacity. A strain rate of 0.00065 s-1 was used, and each tension specimen was stressed until fracture occurred.

2.4 Fatigue cycling and residual strength tests Residual strength testing involved constant amplitude tension-tension fatigue cycling that was prematurely stopped before failure, followed by a post-cycling static tensile test. This experiment utilized a full factorial design, with three factors studied at three levels each (Table 1). Factor A, mesostructure, included the three categories seen in Table 1, with unidirectional 0° laminates and bidirectional +30º/-60º and +45º/-45º alternating laminates. Factor B, maximum cycling stress smax as a proportion of mean s0, was studied at three levels of smax/s0 = 0.90, 0.75, and 0.60. Factor C, cycling amount or fatigue life fraction, included n/N = 0.25, 0.50, and 0.75 (where n = number of cycles; N = mean fatigue life). The mean fatigue life used to compute the number of pre-cycles associated with factor C, for each AB factor combination, was determined in a previous experimental study [12] using the same methods and materials. The results associated with the three mesostructures of interest are summarized in Table 2.

Table 1 Factors and levels used in factorial design of residual strength experiment. Factor A: mesostructure q° B: max stress fraction (smax/s0) C: fatigue life fraction (n/N)

Code Ai Bj Ck

6

0 0.60 0.25

Level/Value +45/-45 0.75 0.50

+30/-60 0.90 0.75

Table 2 Summary of fatigue life results for the three mesostructures and three stress levels tested [31]. Values are the sample mean of 4 test specimens; Standard deviation in parentheses; Factor A: Mesostructure (fiber q) 0° +45°/-45° +30°/-60°

Mean Fatigue Life (cycles) Factor B : Max stress level (smax/s0) 0.90 0.75 0.60 315 (39) 1738 (161) 4315 (591) 1155 (86) 4592 (366) 13628 (3463) 1272 (163) 3463 (211) 11547 (900)

All fatigue cycling was performed at a frequency of 0.25 Hz at room temperature in a humidity-controlled environment. Each fatigue test used a constant amplitude load model with a sinusoidal waveform loading pattern, and a minimum cycle load of 1/10 of the maximum load (stress ratio R = 0.1). Tests were completed in accordance with the ASTM D7791 standard [32], with three replicates for each factor combination. In the previously completed fatigue life study, the factorial design included only factors A and B because the tests were continued until specimen failure. In contrast, the current residual strength tests continued for the number of cycles representing the defined fraction of the mean fatigue life N for the specimen, as specified by factor C. Once cycling was stopped, a static tensile test was subsequently conducted in accordance with the ASTM D638 standard [33], as described in Section 2.2.

2.4 SEM fractography Selected fracture surfaces, resulting from tensile testing of pre-cycled specimens, were prepared by gold sputtering and inspected using a JSM 500-type JEOL scanning electron microscope (SEM).

3. Experimental Results and Discussion 3.1 Ultimate tensile strength Force-displacement data from the static tensile tests were analyzed, and the mean ultimate tensile strength (s0) was computed from the sample of 16 specimens for each mesostructure. The results, seen in Table 3,

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validate previous results [29] and support the conclusion that specimen tensile strength is dependent on the directional processing and FDM specimen mesostructure.

Table 3 Summary of static tensile strength (s0) results. Fiber q, Mesostructure 0° +45°/-45° +30°/-60°

Mean s0 (MPa) 25.15 16.90 14.62

Std deviation (MPa) 1.23 0.60 0.56

3.2 Post-cycling residual strength The residual strength of each test specimen was determined as the ultimate tensile strength obtained . A sample of three specimens was tested for each factor combination. The experimental results are summarized in Table 4, including the mean strength of the three tested specimens and the associated standard deviation.

Table 4 Summary of residual strength results for each ABC factor combination. Standard deviation in parentheses. Factor A: Mesostructure (fiber q)

Factor B: Stress level (smax/s0)

0°

0.90 0.75 0.60 0.90 0.75 0.60 0.90 0.75 0.60

+45/-45°

+30/-60°

Mean residual strength (MPa) Factor C : Fatigue life fraction (n/N) 0.25 0.50 0.75 24.60 (0.61) 24.34 (0.66) 23.84 (0.82) 24.63 (0.24) 24.19 (0.21) 23.06 (0.28) 24.58 (0.26) 23.43 (0.24) 21.85 (0.34) 16.95 (0.14) 16.65 (0.05) 16.19 (0.26) 16.77 (0.16) 16.69 (0.04) 16.25 (0.29) 16.72 (0.23) 16.32 (0.23) 15.26 (0.80) 15.05 (0.39) 14.83 (0.44) 14.58 (0.11) 14.93 (0.05) 14.62 (0.13) 14.29 (0.36) 14.81 (0.46) 14.28 (0.49) 13.55 (0.39)

A graphical representation of the experimental results is shown in Fig. 2. In this figure, the mean residual strength has been normalized with respect to the static strength (Table 3), and the fatigue life fraction is used to represent the number of loading cycles normalized with respect to fatigue life (Table 2). While data normalization improves the ability to compare factor effects, it is a weakness of this study that the fatigue life for each AB factor combination was determined in a previous study [31]. As a result, different 8

spools of FDM ABS were used to determine fatigue life than to study residual strength, and it is likely that there is inter-spool variation that may affect fatigue performance. While this would affect the absolute number of cycles associated with each level of factor C for each AB factor combination, it is not expected to influence the relative comparisons of different mesostructures and stress level.

(a)

(b)

(c)

Fig. 2. Experimental results. Normalized residual strength of 0°, +45/-45°, and +30/-60° mesostructures.

The data curves in Fig. 2 exhibit a decrease in residual strength as the amount of pre-cycling (factor C) increases and the damage accumulates. The normalized strength monotonically decreases with the increase in the percentage of fatigue life for which it is cycled, and the rate of decrease appears most severe for the lowest stress level (0.6 s0). Fig.2 also displays an increased rate of normalized strength degradation as life-fraction increases. This suggests that strength decreases at a higher rate for a specimen that has experienced more damage. In addition, the rate at which strength deteriorates in the first 25% of life appears noticeably greater for the 0° specimens than for the bidirectional mesostructures. This trend in damage rate is also visible for the second quartile of life.

A two-way ANOVA was used to investigate the data trends and assess the equivalence of the mean normalized residual strength for the treatment factor combinations presented in Table 4. Results revealed that all three main effects (A, B, and C) are significant at a level of a = 0.05 [34], suggesting that the residual strength of FDM-ABS components is affected by mesostructure, stress level, and fatigue life 9

fraction. In addition, the BC interaction effect was determined to be significant, F(4,54) = 7.13, p = 0.000, which suggests that the relative influence of maximum cycling stress is different for each fatigue life fraction, and vice-versa. Subsequent post hoc Tukey analyses [34] indicated that the relative effect of the three factors on the mean response is significant (at a = 0.05) for all pairwise comparisons except for those between the +45/-45° and +30/-60° mesostructures, and the 0.90 and 0.75 stress level.

The interaction plot in Fig. 3 displays the relative differences between factor effects that were detected in the data and the statistical analysis. The top two panels of the interaction plot highlight the similarities between the normalized strength of +45/-45° and +30/-60° bidirectional mesostructures relative to both cycling stress and fatigue life fracture. They also illustrate the higher normalized strengths (vertical location) of the bidirectional versus the 0° parts. The steeper slope of the 0° mesostructure line in the first quartile of fatigue life, as seen in the top right panel of Fig. 3, highlights the higher rate of strength deterioration detected in the data. The bidirectional specimens, in contrast, experience a much smaller

Fig. 3. Interaction effects plot. Normalized residual strength (data means) for 0°, +45/-45°, and +30/-60° mesostructures.

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rate of strength loss (statistically significant at a = 0.05) than the 0° parts during the first 25% of fatigue life. The lower panel in Fig. 3 displays the more significant rate of change (steeper slopes) of the residual strength of components cycled at smax = 0.6 s0, as previously noted in discussion of the data results (Fig. 2), and identified in the statistical analysis as the significant BC interaction effect.

The fracture surfaces of pre-cycled specimens subjected to tensile tests were examined and found to display multiple damage modes that varied in prevalence depending on mesostructure. All specimens displayed some level of crazing indicative of brittle failure. The 0° mesostructure was dominated by fiber crazing and cracking (Fig. 4(a)), and displayed a rough fracture surface appearance due to variable fractured-fiber lengths and inconsistent crack paths. The inconstant size of air voids and bonds strength affects the observed damage modes. The bidirectional mesostructures displayed mixed mode repeated failure of tension and shearing (Fig. 4(b)). As noted in previous examinations of specimens failing in static tension or fatigue life tests [29], the fractured surfaces had a sawtooth appearance with individual fibers fracturing normal to their length. Inconsistent inter-raster bonding and void changes appear to influence shearing between fibers and drive the dynamic transition between failure modes.

(a)

(b)

Fig. 4. SEM images of fracture surfaces from tensile tests of pre-cycled specimens. (a) 0° and (b) +45/-45°.

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4. Strength and Fatigue Life Distributions From a phenomenological standpoint, the fatigue damage of cycled components can be evaluated by the deterioration of residual stiffness or strength relative to loading parameters such as stress ratio R, maximum cycling stress smax, and number of loading cycles n. The authors previously studied the deterioration of FDM-ABS stiffness during fatigue cycling and found similarities with the damage evolution experienced by fiber-reinforced composites [31]. This paper examines the deterioration of the initial static strength during cyclic loading, with the aim of predicting the amount of remaining life for which components can support external load. Unlike component stiffness, however, which can be measured nondestructively with every loading cycle, only a single strength measurement is possible for each fatigue test. With smaller amounts of experimental data, strength-based wear-out models in the literature (for composite materials) are often statistical in nature and based on several assumptions regarding static strength, fatigue life, and failure [25]. The following assumptions are similarly made in this study of the residual strength of FFF specimens: 1) Static strength distribution: The scatter in monotonic strength s0 is represented by a twoparameter Weibull distribution [35]; 2) Strength-life-equal-rank: A specimen’s fatigue life is proportional to its static strength, or it has the same rank in static strength and fatigue life [36]; 3) Fracture condition: Fatigue failure occurs when a component’s residual strength decreases to the maximum cycling stress [37].

4.1 Static Strength of FDM Specimens The effectiveness of a two-parameter Weibull distribution to model the scatter in composite material strength has been recognized for many years [38–41]. The monotonic strength s0 of FDM specimens is a random variable that is also assumed to follow a two-parameter Weibull distribution. As such, the probability of finding a static strength value less than or equal to x is given by:

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‫ ݔ‬ఋ ܲሺߪ଴ ൑ ‫ݔ‬ሻ ൌ ͳ െ ݁‫ ݌ݔ‬ቈെ ൬ ൰ ቉ሺͶǤͳሻ ߛ

where g is the scale parameter or characteristic strength and d is the shape parameter.

To test this assumption, a two-parameter Weibull distribution was fit to the experimental static strength data associated with each mesostructure (summarized in Table 3) using a least squares method. The resulting Weibull shape and scale parameters, the Anderson-Darling statistic (AD), and the p-values for the AD [42] are displayed in Table 5. A p-value greater than 0.25, as seen for all three mesostructures, suggests that there is not sufficient evidence to reject the hypothesis that the data fit a two-parameter Weibull distribution.

Table 5 Parameters and fit information for two-parameter Weibull distributions for static strength. Mesostructure Fiber q 0° +45°/-45° +30°/-60°

Weibull parameters and fit scale g 25.71 17.20 14.81

shape d 25.25 34.04 27.54

AD 0.174 0.276 0.327

p-value > 0.25 > 0.25 > 0.25

4.2 Fatigue Life of FDM Specimens When the fatigue life of FDM ABS specimens was previously studied, the relevance of a power-law S-N relationship was validated and similarities between their fatigue-induced stiffness degradation and that of fiber-reinforced composites was revealed [31]. To now study the residual strength evolution of FDM components during cycling, the fatigue response of fiber-based composites [43–49] was again examined and used for comparison. A two-parameter empirical model formulated for CFRP composites with thermosetting resin was selected and evaluated with regard to its ability to describe the degradation of FDM component strength observed during experimental fatigue cycling. The model (Eq.( 4.2)) was developed by D’Amore et al. [50] and is based on the assumption that component strength decays

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continuously as the number of fatigues cycles increases. The strength degradation is linearly dependent on the fatigue stress ratio and is in accordance with a power law, as follows: ߪ଴ െ ߪ௥ ሺ݊ሻ ൌ  ߙߪ௠௔௫ ሺͳ െ ܴሻ൫݊ఉ െ ͳ൯ሺͶǤʹሻ

where s0 is the monotonic tensile strength of the virgin specimens, sr(n) is the residual strength of a

specimen after n cycles of loading, smax is the maximum fatigue cycling stress, R is the cycling stress ratio of smin/smax, and a and b are unknown model parameters that depend on the specimen material and the load conditions [50].

The fracture condition was first applied in order to evaluate the model’s ability to simulate fatigue life and fit an S-N curve to the experimental life data. Specifically, the condition assumes that fatigue failure occurs when residual strength reduces to the maximum cycling stress smax at the fatigue life or n = N cycles (assumption #3 above). This allows for the substitution of n = N and sr(N) = smax into Eq. 4.2), resulting in ߪ଴ ൌ ߪ଴ே ൌ  ߪ௠௔௫ ൣߙሺͳ െ ܴሻ൫ܰఉ െ ͳ൯ ൅ ͳ൧ሺͶǤ͵ሻ

where s0N is the static strength of those specimens that are cycled until they fail at their fatigue life, N.

To investigate the ability of Eq. (4.3) to model the degradation of FDM component strength during cyclic loading, the a and b parameters were estimated using the fatigue life summarized in Table 2. For each of the tested stress levels (Factor B) for a given mesostructure, the value of ߪ଴ே was assumed to be equal to smax (assumption #3), and the value of N was determined experimentally. The resulting a and b

parameters, evaluated using least squares methods (with MATLAB), are displayed in Table 6. In each case, the coefficient of determination (R2) indicates that greater than 97% of the data variability is described by the D’Amore model [50] with the fitted parameter values. The S-N model fit is graphically reported in Fig. 5, where the generated S-N curves are displayed together with the experimental fatigue life data. The data displayed at n = 1 in Fig. 5 are the static strengths associated with each mesostructure.

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Table 6 Least squares parameters for strength degradation model in Eq. (4.3). Mesostructure Fiber q 0° +45°/-45° +30°/-60°

Model parameters and fit a 0.0099 0.0007 0.0009

b 0.495 0.751 0.719

R2 0.977 0.993 0.971

Fig. 5. S-N curves for different mesostructures, including experimental data and cumulative damage model [50].

Based on assumption #2, it is expected that static strength and fatigue life distributions will be related for FDM specimens. To test this assumption and further validate the model, Eq. (4.3) was used together with the fitted a and b values and the fatigue life data to compute the model-generated nominal strength of specimens subjected to cyclic loading until failure, or s0N values [50]. Ordered experimental and computed strength values are displayed in Fig. 6, together with the empirical Weibull distributions.

The experimental static strength data includes sixteen values of s0 for each mesostructure. The sixteen calculated strength values, s0N, are based on four samples of fatigue life data, each associated with a cycling stress smax and each including only four specimens. The observable discrepancies between the shape factors of the two distribution functions can be partly attributed to the sampling of the different data sets and the small sample sizes. 15

(a)

(b)

(c)

Fig. 6. Statistical distributions (2-parameter Weibull) of experimental (s0) and computed (s0N) static strength for (a) 0°, (b) +45/-45°, and (c) +30/-60° mesostructures.

Based on the strength-life equal rank assumption, the experimental and computed data were then merged [49], and the Weibull shape and scale parameters for this larger data set were estimated for each mesostructure. The merged models are displayed in Fig. 7, and the fitted parameters are presented in Table 7. The AD and associated p-values in Table 7 do not contradict the hypothesis that the merged data fit a two-parameter Weibull distribution, which further supports the model assumptions.

(a)

(b)

(c)

Fig. 7. Statistical distributions (2-parameter Weibull) of merged static strength samples (combined experimental and computed) for (a) 0°, (b) +45/-45°, and (c) +30/-60° mesostructures.

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Table 7 Weibull parameters and goodness of fit information for experimental, computed, and merged data. Mesostructure Fiber q 0° +45°/-45° +30°/-60°

Weibull parameters and fit shape g Exp Data Computed 25.25 28.92 34.04 39.91 27.54 31.02

Merged 26.88 34.87 28.88

scale d Exp Data Computed 25.71 25.80 17.20 16.97 14.89 14.94

Merged 25.76 17.09 14.91

AD, p-value for Merged 0.31, >0.25 0.21, >0.25 0.36 , >0.25

5. Residual Strength Degradation Model The literature is rich with research based on the principle that damage accumulates in materials that are subjected to cyclical loading [51]. As the number of loading cycles increases and the damage continues to accrue, the remaining or residual strength of the component decreases. As a result, the residual strength, sr, is a useful parameter with which to assess the damage level. Per the fracture condition, if cycling is continued until failure occurs at fatigue life, N, the residual strength at failure is considered equal to the maximum cycle stress, smax. As such, the S-N curve provides the residual strength for specimens cycled at S = smax until fracture at fatigue life N, or S(N) = sr(N). If cycling is instead stopped prematurely, the residual strength of the specimen is defined as the ultimate tensile stress achieved in a post-cycling tension test. In this more general case, with the number of loading cycles, n, less than the fatigue life N, the residual strength is expected to be greater than S(n) but less than the static strength, or S(n) < sr(n) < s0. Given this inherent relationship between sr(n) and the stochastic variables of static strength s0 and fatigue life N, the strength-life-equal-rank assumption and associated statistical analysis used to consider s0 and N is extended to include sr(n); with all distributions assumed to be 2-parameter Weibull.

In order to evaluate the ability of the D’Amore et al. [50] equation to model strength degradation and predict the residual strength of FDM components subjected to constant amplitude uniaxial fatigue loading, an explicit expression for the residual strength was formed by substituting Eq. (4.3) into Eq. (4.2): 17

ߪ௥ ሺ݊ሻ ൌ ߪ௠௔௫ ൅  ߪ௠௔௫ ߙሺͳ െ ܴሻ൫ܰఉ െ ݊ఉ ൯ሺͷǤͳሻ

This is a monotonically decreasing function that is theoretically equal to s0, or the strength of the virgin specimens for each mesostructure, for the unloaded (n = 0) case, and is equal to smax at the moment of failure (n = N). The a and b parameters in Eq. (5.1) were extracted using a least squares nonlinear regression analysis for each combination of tested levels of factors A (mesostructure) and B (cycling stress). Although the resulting model curves appeared to follow the general trend of the data, the quality of the fit decreased as N increased and the regression analysis had difficulty converging when determining a values that were very close to 0. The model in Eq. (5.1) was subsequently altered by normalizing residual strength by s0 and normalizing the endured number of cycles by fatigue life N, for each AB factor combination. The resulting model for normalized residual strength in Eq. (5.2) has the monotonically decreasing form, but the range is now [smax/s0, 1] and the domain is [0, 1]. The a* parameter in Eq. (5.2) is a scaled version of the original a parameter in Eq. (5.1). ߪ௥ ሺ݊ሻ ߪ௠௔௫ ߪ௠௔௫ ‫כ‬ ݊ ఉ ൌ ൅ ߙ ሺͳ െ ܴሻ ቆͳ െ ቀ ቁ ቇሺͷǤʹሻ ߪ଴ ߪ଴ ߪ଴ ܰ

Further noting that the boundary condition at n = 0 defines the residual strength sr(0) to be equal to s0, and the associated normalized residual strength is thus equal to 1, the a* values are determined to be: ߪ௠௔௫ ሻ ߪ଴ ߙ‫ כ‬ൌ ሺͷǤ͵ሻ ߪ ሺͳ െ ܴሻሺ ௠௔௫ ሻ ߪ଴ ሺͳ െ 

The least squares fitted b parameters are displayed in Table 8 along with the related coefficients of determination (R2 values), and the resulting models and data are displayed graphically in Fig. 8. The R2 values ranged between 0.61 and 0.79, and it is noted that the regression residual pattern displayed some systematic behavior, suggesting that the model may not properly represent the underlying shape of the data for each mesostructure.

18

Table 8 Fitted b parameters for the normalized strength degradation model based on D’Amore et al. [50]. Coefficient of determination, R2, in parentheses; Fitted b-values

Fiber q Mesostructure (Ai) 0° +45°/-45° +30°/-60°

(a)

Maximum fatigue loading (Bj*s0) 0.90 s0 1.67 (0.79) 2.95 (0.79) 4.40 (0.77)

0.75 s0 3.40 (0.77) 6.32 (0.55) 5.53 (0.67)

0.60 s0 3.37 (0.78) 4.68 (0.62) 4.59 (0.61)

(b)

(c)

Fig. 8. Normalized residual strength model, Eqn (5.2), and experimental data for (a) 0°, (b) +45/-45°, and (c) +30/-60° mesostructures. In an effort to improve the model’s capability for FDM specimens and allow it to represent more complex strength-degradation trends, an additional power parameter was incorporated, as seen in Eq. (5.4). ఒ

ߪ௥ ሺ݊ሻ ߪ௠௔௫ ߪ௠௔௫ ‫כ‬ ݊ ఉ ൌ ൅ ߙ ሺͳ െ ܴሻ ቆͳ െ ቀ ቁ ቇ ሺͷǤͶሻ ߪ଴ ߪ଴ ߪ଴ ܰ

When the new parameter l is equal to 1, this model is the same as that in Eq. (5.2). More generally, the

model in Eq. (5.4) has the same boundary conditions as Eq. (5.2), with normalized residual strength equal to 1 for n = 0, and equal to srmax/s0 for n = N. The a* values are thus found using Eq. (5.3).

The least squares fitted b and l parameters are displayed in Table 9 along with the related coefficients of determination, and the new models are displayed graphically in Fig. 9 with the FDM data.

19

Table 9 Fitted parameters b and l for the model in Eq. (5.4), with R2-values in parentheses. Fitted b and l-values Fiber q Mesostructure 0° +45°/-45° +30°/-60°

Maximum fatigue loading (Bj*s0) 0.90s0 0.581, 0.381, (0.941) 2.448, 0.835, (0.811) 2.905, 0.549 (0.801)

0.85

0.90 s 0

0.8

Data 0.90 s 0 0.75 s 0

0.75 0.7 0.65

Data 0.75 s 0 0.60 s 0

0.6

Data 0.60 s 0

0.55 0

0.2

0.4

0.6

Fatigue Life fraction (n/N)

0.8

1

Norm Residual Strength (s r(n)/s 0)

0.9

0.60s0 1.273, 0.339, (0.963) 1.942, 0.329, (0.787) 1.451, 0.256, (0.766)

1

1

0.95

Norm Residual Strength (s r(n)/s 0)

Norm Residual Strength (s r(n)/s 0)

1

0.75s0 1.077, 0.317, (0.920) 1.663, 0.170, (0.769) 1.455, 0.194, (0.917)

0.95 0.9

0.90 s 0

0.85

Data 0.90 s 0 0.75 s 0

0.8 0.75

Data 0.75 s 0 0.60 s 0

0.7

0.65

Data 0.60 s 0

0.6

0.95 0.9

0.90 s 0

0.85

Data 0.90 s 0 0.75 s 0

0.8 0.75 0.7

Data 0.75 s 0 0.60 s 0

0.65

Data 0.60 s 0

0.6 0.55

0.55 0

0.2

0.4

0.6

Fatigue Life fraction (n/N)

(a)

(b)

0.8

1

0

0.2

0.4

0.6

0.8

1

Fatigue Life fraction (n/N)

(c)

Fig. 9. Revised normalized residual strength model, Eqn (5.4), and experimental data for (a) 0°, (b) +45/-45°, and (c) +30/-60° mesostructures.

While the additional parameter reduces the model simplicity, examination of the results in Table 9 reveals the improved ability of this model to describe the FDM residual strength data variability. The R2 values for all factor combinations has increased, in comparison with Eq. (5.2), with an overall range of 0.77 to 0.96. The new model achieves its best results describing the degradation of strength for the 0° unidirectional mesostructure (0.91 < R2 < 0.96). Comparison of Figs. 8 and 9 reveals differences in the curve shapes associated with the two models for this mesostructure, including a notable decrease in the slopes in the first quartile of fatigue life in the new model.

Finally, in an effort to improve the ability to make relative comparisons of strength degradation trends for different mesostructures, a mathematical normalization process was applied to Eq. 5.4 to create transformed curves (one for each smax value) with the same boundary conditions. This is done by 20

considering the difference between the residual strength and the maximum cycling stress, or the strength reserve. The normalized strength reserve (NSR) associated with the number of pre-cycles n, is defined by Stojković et al. [51] as ܴܰܵሺ݊ሻ ൌ

ߪ௥ ሺ݊ሻ െ  ߪ௠௔௫ ሺͷǤͷሻ ߪ଴ െ  ߪ௠௔௫

and it provides a relative measure of the proportion of residual strength remaining in a specimen that is being cycled at a stress of smax. Using the residual strength model in Eq. (5.4), the normalized strength reserve is expressed as ܴܰܵሺ݊ሻ ൌ 

ఒ

ߙ ‫ߪ כ‬௠௔௫ ሺͳ െ ܴሻ ݊ ఉ ቆͳ െ ቀ ቁ ቇ ሺͷǤ͸ሻ ߪ଴ െ  ߪ௠௔௫ ܰ

Noting that smax is a proportion of s0, as defined by the relevant level of experimental factor B, Eq. (5.6) can be rewritten as ܴܰܵሺ݊ሻ ൌ 

ߙ ‫ כ‬ሺͳ െ ܴሻ ቀ ͳ െቀ

ߪ௠௔௫ ቁ ߪ଴

ߪ௠௔௫ ቁ ߪ଴

ఒ

݊ ఉ ቆͳ െ ቀ ቁ ቇ ሺͷǤ͸ܽሻ ܰ

with smax/s0 = 0.90, 0.75, or 0.60 for the experimentation in this study. The parameters a*, b, and l are

associated with the level of factor B for a given mesostructure (factor A). Also noting the definition of a* in Eq. (5.3), the NSR(n) in Eq. (5.6a) further simplifies to Eq. (5.6b). ఒ

݊ ఉ ܴܰܵሺ݊ሻ ൌ  ቆͳ െ ቀ ቁ ቇ ሺͷǤ͸ܾሻ ܰ

The least squares fitted b and l parameters for each AB factor combination are the same as those found for the normalized residual strength model in Eq. (5.4), displayed in Table 9 above. The resulting NSR(n) curves and experimental data are displayed graphically in Fig. 10. The curves provide a useful means by which to determine a normalized measure of the remaining available strength in a part that is undergoing constant amplitude fatigue cycling. As seen in Fig. 10, NSR(n) captures the data trends for the 0° 21

mesostructure and highlights their higher relative loss of strength in the first quartile of life in comparison with the bidirectional mesostructures. The initial loss of strength is followed by a period in which the degradation rate is smaller, before a sudden increase in rate of strength degradation prior to fracture. This three-phased strength degradation pattern is most apparent for the 0.90 s0 stress level. The curve further demonstrates the relevance of introducing the additional power parameter l, and mimics the stiffness degradation patterns revealed in previous work [31]. This is also the damage accumulation pattern often seen in CFRP and other composite materials [51].

(a)

(b) Fig. 9.

(c)

Normalized strength evolution model and experimental data for (a) 0°, (b) +45/-45°, and (c) +30/-60° mesostructures.

6. Conclusions The fatigue damage of additive manufactured ABS specimens subjected to uniaxial constant-amplitude loading was characterized. Interrupted tension-tension fatigue tests were used to examine the 22

deterioration of tensile strength experienced by three FDM mesostructures subjected to different levels of cycling stress and fatigue life fraction. The scatter affecting fatigue life and residual strength data required a statistical approach for damage modeling. A strength degradation model originally developed for CFRP laminates [50] was modified to represent the normalized residual strength of FDM specimens subjected to fatigue loading. In addition, the normalized strength reserve was developed as a tool by which to compare the relative strength degradation trends associated with different cycling stress levels for a given mesostructure.

The following conclusions have been drawn: (a)

The residual strength of FDM specimens monotonically decreases as damage accumulates with increased amounts of constant-amplitude tensile fatigue cycling. The degradation of normalized residual strength occurs at a greater rate for the 0° unidirectional parts than for the +45/-45° and +30/-60° bidirectional mesostructures. The difference in the decrease in the strength of the 0° versus the bidirectional laminates is statistically significant (a = 0.05).

(b)

The normalized residual strengths of the bidirectional +45/-45° and +30/-60° mesostructures are statistically equal (a = 0.05) for all factor combinations of cycling stress and fatigue life fracture, and are statistically greater (a = 0.05) than that of the 0° parts. However, the actual residual tensile strength of the 0° parts is greater than both +45/-45° and +30/-60° mesostructures, for all factor combinations of cycling stress and fatigue life fracture, due to the alignment of the fibers with the load direction.

(c)

A nonlinear strength degradation model (Eq. (5.4)), based on the fatigue behavior of CFRP composites, effectively captures the characteristics of the damage accumulation of fused filament deposited ABS subjected to tension-tension constant-amplitude cyclic loading. The additional fitted power parameter (l) varies from 1.0 for all factor combinations, suggesting that the normalized data trends differ from those represented in the original CFRP model (Eq. (5.1)).

23

Coefficients of determination (R2) indicate a stronger model fit for the 0° unidirectional laminates than for the +45°/-45° and +30°/-60° bidirectional mesostructures.

The ability to accurately model the accumulated damage of FDM specimens is very important for the informed design of commercial products that include FFF parts. Additional research is planned to investigate the influence of fatigue stress ratio R on strength degradation. To increase the practical impact of this work, the study of the strength degradation response of FDM parts to variable amplitude loading is also needed.

Acknowledgements The authors acknowledge funding provided by the National Science Foundation, DUE-1317446, by way of Bucknell’s STEM Scholars program, and support from Bucknell University through a Presidential Professorship for C. W. Ziemian. The authors also thank the following students for their assistance performing a portion of the tension and fatigue testing: Matthew Benjamin (Rensselaer Polytechnic Institute), Patricia Cupay (Bucknell University), and David Zhou (Bucknell University).

Data Availability The raw data required to reproduce these findings are available to download from [https://data.mendeley.com/datasets/skkxgbst5h/draft?a=3862c0f3-0b80-4a1c-b1d9-09a6bec68836].

24

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27

Graphical Abstract

Highlights: !

Fiber orientation and layering pattern affect strength degradation of fatigue loaded FDM parts.

!

Rate of normalized strength degradation is higher for 0° parts than bidirectional mesostructures.

!

Normalized residual strengths of bidirectional parts are greater than that of 0° parts.

!

A nonlinear phenomenological model predicts residual strength for the studied factor levels.

*Declaration of Interest Statement

Declaration of interests ‫ ܈‬The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: