The Essential Work of Fracture Parameters for 3D printed polymer sheets

A. D\'iaz; E. Martinez-Pa\~neda; I.I. Cuesta; J.M. Alegre

arxiv: 1906.11512 · v1 · pith:JKVBRHFEnew · submitted 2019-06-27 · ⚛️ physics.app-ph · cond-mat.mtrl-sci

The Essential Work of Fracture Parameters for 3D printed polymer sheets

I.I. Cuesta , E. Martinez-Pa\~neda , A. D\'iaz , J.M. Alegre This is my paper

Pith reviewed 2026-05-25 14:13 UTC · model grok-4.3

classification ⚛️ physics.app-ph cond-mat.mtrl-sci

keywords fracturepolymerpolymersadditivemanufacturingsheetsadditivelydden-sp

0 comments

The pith

Fiber-reinforced Onyx 3D printed sheets exhibit an order of magnitude higher essential work of fracture than unreinforced PLA, PP and ABS, and a miniature DDEN-SP specimen produces results aligned with standard DDEN-T tests.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Researchers printed sheets from four polymers and cut deeply notched tensile specimens to measure how much energy is needed to start and grow a crack. The fiber-reinforced Onyx material required far more energy to break than the three standard polymers. They also developed a smaller punch-style specimen that uses much less material yet gave similar toughness numbers. The work shows that adding fibers changes the way cracks move through the printed layers. Because 3D printing builds parts layer by layer, the direction of printing and the presence of fibers both affect how the material resists breaking. The miniature test lets labs screen new print settings or materials when only small amounts of filament are available.

Core claim

fibre-reinforcement translates into a notable increase in fracture resistance, with the fracture energy of Onyx being an order of magnitude higher than that reported for non-reinforced polymers. The results obtained exhibit good alignment with the DDEN-T data, suggesting the suitability of the DDEN-SP test.

Load-bearing premise

The assumption that the Essential Work of Fracture method, developed for conventional polymers, applies without modification to additively manufactured layered materials whose properties vary with print direction and that the miniature DDEN-SP geometry produces equivalent results without unaccounted size or constraint effects.

read the original abstract

Additive manufacturing is becoming increasingly popular in academia and industry. Accordingly, there has been a growing interest in characterizing 3D printed samples to determine their structural integrity behaviour. We employ the Essential Work of Fracture (EWF) to investigate the mechanical response of polymer sheets obtained through additive manufacturing. Our goal is twofold; first, we aim at gaining insight into the role of fibre reinforcement on the fracture resistance of additively manufactured polymer sheets. Deeply double-edge notched tensile (DDEN-T) tests are conducted on four different polymers: Onyx, a crystalline, nylon-reinforced polymer, and three standard polymers used in additive manufacturing - PLA, PP and ABS. Results show that fibre-reinforcement translates into a notable increase in fracture resistance, with the fracture energy of Onyx being an order of magnitude higher than that reported for non-reinforced polymers. On the other hand, we propose the use of a miniature test specimen, the deeply double-edge notched small punch specimens (DDEN-SP), to characterize the mechanical response using a limited amount of material. The results obtained exhibit good alignment with the DDEN-T data, suggesting the suitability of the DDEN-SP test for measuring fracture properties of additively manufactured polymers in a cost-effective manner.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Onyx shows roughly 10x higher fracture energy than PLA/PP/ABS in EWF tests on 3D printed sheets, and the miniature DDEN-SP geometry lines up with standard DDEN-T, but the method's core assumptions are not checked for these layered anisotropic materials.

read the letter

The main thing to know is that this paper measures essential work of fracture on four 3D printed polymers and reports that the fiber-reinforced Onyx has fracture energy an order of magnitude above the unreinforced PLA, PP, and ABS, while also showing that a small-punch style specimen (DDEN-SP) produces numbers close to the usual DDEN-T tensile tests. That comparison and the low-material geometry are the concrete new pieces here. The work applies an established technique to a practical setting where material is often scarce, and the reported alignment between geometries is a useful data point for anyone screening printed polymers. It gives actual numbers rather than just qualitative claims, which is worth having in the additive manufacturing literature. The soft spot is the lack of verification that EWF conditions hold. These printed sheets are orthotropic laminates with direction-dependent properties, unlike the isotropic polymers the method was built for. The paper does not show full ligament yielding before crack growth, self-similar load-displacement curves across ligament lengths, or checks for size or constraint effects in the miniature specimen. Without those, the extrapolated w_e values and the geometry agreement are harder to trust at face value. Print parameters, error bars, and statistical detail are also thin in what is visible. This is for readers working on structural testing of additively manufactured parts who need fracture numbers for design or material selection. It will not shift fracture mechanics broadly, but the experimental comparison is worth referee time even if the analysis needs tightening on the anisotropy question. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The paper applies the Essential Work of Fracture (EWF) method to 3D-printed polymer sheets, performing DDEN-T tests on fiber-reinforced Onyx and unreinforced PLA, PP, and ABS. It reports that Onyx exhibits an order-of-magnitude higher fracture energy due to fiber reinforcement. It also introduces a miniature DDEN-SP geometry, claiming good agreement with DDEN-T results and suitability for limited-material characterization of AM polymers.

Significance. If the EWF assumptions are shown to hold, the work would provide concrete evidence that short-fiber reinforcement substantially raises fracture resistance in AM polymers and would validate a small-scale test geometry, both of which are useful for practical material selection and design with limited feedstock.

major comments (2)

[Results / Discussion (EWF analysis)] The central claim that Onyx fracture energy is an order of magnitude higher rests on direct application of the EWF relation w = w_e + β w_p l. No section demonstrates that the prerequisites (complete ligament yielding prior to crack advance and self-similar normalized load-displacement curves across ligament lengths) are satisfied for these orthotropic, layered materials whose stiffness and yield behavior vary with print direction. Without such verification the extracted w_e values and the reported difference versus unreinforced polymers cannot be taken as physically comparable.
[DDEN-SP validation section] The suitability of the miniature DDEN-SP geometry is asserted on the basis of numerical alignment with DDEN-T data. The manuscript provides no size-effect study, no assessment of plane-strain constraint differences, and no check that plastic-zone confinement remains valid at the reduced scale. These omissions are load-bearing for the claim that DDEN-SP produces equivalent fracture parameters.

minor comments (2)

[Experimental methods] Print parameters (layer height, infill pattern, raster angle) and specimen dimensions are not tabulated; these details are required to assess anisotropy effects and to allow replication.
[Tables / Figures] Error bars, number of replicates, and any statistical treatment of the w_e and β w_p values are absent from the reported data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the detailed and constructive feedback on our manuscript. We address the major comments below, indicating the revisions we plan to make to address the concerns raised.

read point-by-point responses

Referee: [Results / Discussion (EWF analysis)] The central claim that Onyx fracture energy is an order of magnitude higher rests on direct application of the EWF relation w = w_e + β w_p l. No section demonstrates that the prerequisites (complete ligament yielding prior to crack advance and self-similar normalized load-displacement curves across ligament lengths) are satisfied for these orthotropic, layered materials whose stiffness and yield behavior vary with print direction. Without such verification the extracted w_e values and the reported difference versus unreinforced polymers cannot be taken as physically comparable.

Authors: We agree that demonstrating the validity of the EWF assumptions is crucial, especially for the anisotropic nature of the 3D-printed materials. Although the original manuscript focused on the application and results, we will revise the Results and Discussion section to include explicit verification. Specifically, we will add normalized load-displacement curves to show self-similarity across ligament lengths and provide evidence (e.g., from high-speed imaging or strain field analysis) that complete ligament yielding occurs prior to crack propagation. We will also discuss the print orientation used and its effect on the measured properties. These additions will strengthen the comparability of the w_e values. revision: yes
Referee: [DDEN-SP validation section] The suitability of the miniature DDEN-SP geometry is asserted on the basis of numerical alignment with DDEN-T data. The manuscript provides no size-effect study, no assessment of plane-strain constraint differences, and no check that plastic-zone confinement remains valid at the reduced scale. These omissions are load-bearing for the claim that DDEN-SP produces equivalent fracture parameters.

Authors: We acknowledge the need for a more rigorous validation of the DDEN-SP geometry. In the revised manuscript, we will expand the validation section to include a discussion of the plastic zone size relative to the specimen dimensions to confirm confinement, and address potential differences in constraint between the geometries. While a full size-effect study may require additional experiments beyond the current scope, we will provide supporting analysis based on the existing data and literature on similar small-scale tests. This will better substantiate the claim of equivalence. revision: partial

Circularity Check

0 steps flagged

No circularity: purely experimental application of established EWF protocol to measured data

full rationale

The paper reports direct experimental measurements of fracture energy via the standard EWF relation w = w_e + β w_p l on DDEN-T and DDEN-SP specimens for four polymers. No derivations, predictions, or uniqueness theorems are claimed; the reported order-of-magnitude increase for Onyx and the alignment between geometries are empirical observations from load-displacement curves. No self-citations, fitted inputs renamed as predictions, or ansatzes appear in the load-bearing steps. The work is self-contained against external benchmarks as a measurement study.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the Essential Work of Fracture procedure remains valid for additively manufactured layered polymers and that the miniature specimen geometry does not introduce uncharacterized constraint or size effects.

axioms (1)

domain assumption The Essential Work of Fracture method applies directly to 3D printed polymer sheets without modification for layer anisotropy.
Invoked when the authors interpret DDEN-T and DDEN-SP results as direct measures of fracture resistance.

pith-pipeline@v0.9.0 · 5768 in / 1230 out tokens · 24949 ms · 2026-05-25T14:13:19.610492+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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A.B. Martinez, J. Gamez-Perez, M. Sanchez-Soto, J.I. Velasco, O.O. Santana, M. Ll. Maspoch. The Essential Work of Fracture (EWF) method – Analyzing the Post-Yielding Fracture Mechanics of polymers. Engineering Failure Analysis, 16, pp. 2604-2617. (2009)

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[1] [1]

Quan et al

Z. Quan et al. Printing direction dependence of mechanical behavior of additively manufactured 3D preforms and composites. Composite Structures 184 (2018) 917-923

work page 2018

[2] [2]

Zhao et al

G. Zhao et al. Mechanical properties of Sn63Pb37 components by fused coating technology. Additive Manufacturing 22 (2018) 388–393

work page 2018

[3] [3]

Al Abadi et al

H. Al Abadi et al. Elastic properties of 3D printed fibre -reinforced structures . Composite Structures 193 (2018) 8-18

work page 2018

[4] [4]

Hou et al

Z. Hou et al. 3D printed continuous fibre reinforced composite corrugated structure. Composite Structures 184 (2018) 1005-1010

work page 2018

[5] [5]

Panda et al

B. Panda et al. Experimental and numerical modelling of mechanical properties of 3D printed honeycomb structures. Measurement 116 (2018) 495–506. 18

work page 2018

[6] [6]

3D printing of polymer matrix composites: A review and prospective

Wang X., et al. 3D printing of polymer matrix composites: A review and prospective. Composites Part B 110, (2017) 442-458

work page 2017

[7] [7]

Melenka et al

G.W. Melenka et al. Evaluation and prediction of the tensile properties of continuous fiber - reinforced 3D printed structures. Composite Structures 153 (2016) 866-875

work page 2016

[8] [8]

Chacón et al

J.M. Chacón et al. Additive manufacturing of PLA structures using fused deposition modelling: Effect of process parameters on mechanical properties and their optimal selection. Materials & Design 124 (2017) 143–157

work page 2017

[9] [9]

J. Wang, H. Xie, Z. Weng, T. Senthil, L. Wu. A novel approach to improve mechanical properties of parts fabricated by fused deposition modelling. Materials & Design 105 (2016) 152-159

work page 2016

[10] [10]

M. A. Ryder et al. Fabrication and properties of novel polymer -metal composites using fused deposition modeling. Composites Science and Technology 158 (2018) 43–50

work page 2018

[11] [11]

Arbeiter et al

F. Arbeiter et al. Fracture mechanical characterization and lifetime estimation of nearhomogeneous components produced by fused filament fabrication. Polymer Testing 66 (2018) 105–113

work page 2018

[12] [12]

Aliheidari et al

N. Aliheidari et al. Fracture resistance measurement of fused deposition modeling 3D printed polymers. Polymer Testing 60 (2017) 94–101

work page 2017

[13] [13]

J. M. Puigoriol -Forcada et al. Flexural fatigue properties of polycarbonate fused -deposition modelling specimens. Materials & Design 155 (2018) 414–421

work page 2018

[14] [14]

A. G. Salazar-Martín, M. A. Pérez, A.-A. García-Granada, G. Reyes, J. M. Puigoriol-Forcada. A study of creep in polycarbonate fused deposition modelling parts. Materials & Design 141 (2018) 414–425

work page 2018

[15] [15]

Kumar et al

R. Kumar et al. Investigations of mechanical, thermal and morphological properties o f FDM fabricated parts for friction welding applications. Measurement 120 (2018) 11–20

work page 2018

[16] [16]

J.M. Baik, J. Kameda, O. Back, Small Punch Test evaluation of intergranular embrittlement of an alloy steel, Scr. Metall. et Mater. 17 (1983) 1443-1447. 19

work page 1983

[17] [17]

Martínez-Pañeda, T.E

E. Martínez-Pañeda, T.E. García, C. Rodríguez. Fracture toughness characterization through notched small punch test specimens. Materials Science and Engineering A, 657, pp. 422 -430 (2016)

work page 2016

[18] [18]

Cuesta, J.M

I.I. Cuesta, J.M. Alegre, V. Ortega -López, Polymer pre -notched sma ll punch specimens to evaluate the essential work of fracture (EWF) parameters, Material and Design 83 (2015) 363-367

work page 2015

[19] [19]

Broberg, Crack-growth criteria and non-linear fracture mechanics, J

K.B. Broberg, Crack-growth criteria and non-linear fracture mechanics, J. Mech. Phys. Solids 19 (1971) 407-418

work page 1971

[20] [20]

Broberg, On stable crack growth, J

K.B. Broberg, On stable crack growth, J. Mech. Phys. Solids 23 (1975) 215-237

work page 1975

[21] [21]

Y.W. Mai, B. Cotterell, The essential work of fracture for tearing of ductile metals, Int. J. Fracture 24 (1984) 229-236

work page 1984

[22] [22]

Y.W. Mai, B. Cotterell, On the essential work of ductile fracture in polymers, Int. J. Fracture 32 (1986) 105-125

work page 1986

[23] [23]

Wang, R.K.Y

X.L. Wang, R.K.Y. Li, Y.X. Cao, Y.Z. Meng, Essential work of fracture analysis for starch filled poly(propylene carbonate) composites, Mater. & Design 28 (2007) 1934-1939

work page 2007

[24] [24]

Martinez, J

A.B. Martinez, J. Gamez-Perez, M. Sanchez-Soto, J.I. Velasco, O.O. Santana, M.Ll. Maspoch, The essential work of fracture (EWF) method – Analyzing the post-yielding fracture mechanics of polymers, Eng. Fail. Anal. 16 (2009) 2604-2617

work page 2009

[25] [25]

Bárány, T

T. Bárány, T. Czigány, J. Karger-Kocsis, Application of the essential work of fracture (EWF) concept for polymers, related blends and composites: A review, Progress in Polym. Sci. 35 (2010) 1257-1287

work page 2010

[26] [26]

Mai, S.C

Y.W. Mai, S.C. Wong, X.H. Chen, Application of fracture mechanics for characterization of toughness of polymer blends. In: Paul DR, Bucknall CB (Eds.), Polymer blends: formulations and performance, Vol 2, Wiley, New York, 2000, pp. 17–58

work page 2000

[27] [27]

Cuesta, J.M

I.I. Cuesta, J.M. Alegre, New fracture characterization in polymer miniature specimens based on the essential work of fracture, J. Appl. Polym. Sci. 133 (2016) 42837-42841

work page 2016

[28] [28]

X. Mao, H. Takahashi, Development of a further-miniaturized specimen of 3 mm diameter for tem disk small punch tests, J. Nucl. Mater. 150 (1987) 42-52. 20

work page 1987

[29] [29]

Saucedo-Muñoz, S

M.L. Saucedo-Muñoz, S. Cheng Liu, T. Hashida, H. Takahashi, H. Nakajima, Correlationship between JIc and equivalent fracture strain determined by small -punch tests in JN1, JJ1 and JK2 austenitic stainless steels, Cryogenics 41 (2001) 713-719

work page 2001

[30] [30]

Bulloch, A review of the ESB small punch test data on various plant components with special emphasis on fractographic details, Eng

J.H. Bulloch, A review of the ESB small punch test data on various plant components with special emphasis on fractographic details, Eng. Fail. Anal. 9 (2002) 511-534

work page 2002

[31] [31]

J.B. Ju, J. Jang, D. Kwon, Evaluation of fracture toughness by small-punch testing techniques using sharp notched specimens, Int. J. of Press. Vessels Pip. 80 (2003) 221-228

work page 2003

[32] [32]

Cuesta, A

I.I. Cuesta, A. Willig, A. Díaz, E. Martínez-Pañeda, J.M. Alegre. Pre-notched dog bone small punch specimens for the estimation of fracture properties. Engineering Failure Analysis, 96, pp. 236-240 (2019)

work page 2019

[33] [33]

CEN Workshop Agreement, CWA 15627:2007 D/E/F, Small Punch Test Method for Metallic Materials, CEN, Brussels Belgium, 2007

work page 2007

[34] [34]

Martinez, J

A.B. Martinez, J. Gamez-Perez, M. Sanchez-Soto, J.I. Velasco, O.O. Santana, M. Ll. Maspoch. The Essential Work of Fracture (EWF) method – Analyzing the Post-Yielding Fracture Mechanics of polymers. Engineering Failure Analysis, 16, pp. 2604-2617. (2009)

work page 2009