Ultra-strong and damage tolerant metallic bulk materials: A lesson from nanostructured pearlitic steel wires

Structural materials used for safety critical applications require high strength and simultaneously high resistance against crack growth, referred to as damage tolerance. However, the two properties typically exclude each other and research efforts towards ever stronger materials are hampered by drastic loss of fracture resistance. Therefore, future development of novel ultra-strong bulk materials requires a fundamental understanding of the toughness determining mechanisms. As model material we use today’s strongest metallic bulk material, namely, a nanostructured pearlitic steel wire, and measured the fracture toughness on micron-sized specimens in different crack growth directions and found an unexpected strong anisotropy in the fracture resistance. Along the wire axis the material reveals ultra-high strength combined with so far unprecedented damage tolerance. We attribute this excellent property combination to the anisotropy in the fracture toughness inducing a high propensity for micro-crack formation parallel to the wire axis. This effect causes a local crack tip stress relaxation and enables the high fracture toughness without being detrimental to the material’s strength.


a) Fractographic investigations
The fractography was investigated with a scanning electron microscope (SEM) using a LEO (Zeiss) 1525 equipped with a field emission gun operated with acceleration voltages between 3-20 kV depending on the used detector signal and magnification. As a further measure for the fracture toughness the crack tip opening displacement for crack initiation, CTODi, was evaluated for the perpendicular orientation in order to compare and confirm the values of the stress based analyses. This local estimate of the fracture toughness could be directly inferred from the fracture surface, see example taken from the "low deformed" wire in Fig. S1. For Fig. S1, SEM-image pairs were recorded from the same position under different tilt angles on both fracture halves. The area of interest for that was particularily the transition from the pre-crack introduced by FIB-milling to the overload fracture zone. From these images 3-dimensional surface models could be calculated using a software from MeX, Alicona (Fig. S1a). From the 3D-models, representing the exact same area on both fracture halves, arbitrary crack paths taken along identical features on both fracture halves were defined (Fig.   S1b). These crack paths deliver height profiles, which allow the reconstruction of the fracture process commencing from the blunting process and to indentify the exact point at which the pre-crack coalesces with the first void or nanocrack ahead of the crack tip, representing CTODi (Fig. S1c). Further details regarding the evaluation procedure and the underlying techniques can be found elsewhere 1,2 .
The CTODi, stemming from elasto-plastic fracture mechanic methodologies, can also be used to calculate the equivalent fracture toughness for the linear elastic case according to 3 : Depending on the wire-diameter for the ultimate strength 7 or 4 GPa is taken, for the Young's Modulus, E, a typical value of 210 GPa, the Poisson's ratio,  as 0.3 and for the parameter, m, a typical value of 2 for plane strain conditions. The same procedure was also applied for the high-deformed state in the same testing direction and an example is presented in  The maximum stress 22 is much higher than the uniaxial flow stress as a consequence of the multiaxial stress state and is risen by a factor of almost 3 considering a non-hardening material which is a good approximation for the present case. Delaminations reduce 33 and as a consequence also 11 and 22.

c) Ashby map design
The Ashby map was partly reproduced from Ashby's book "Material selection in mechanical design"

d) Plastic zone sizes
For all fracture toughness values the size of the plastic zone was calculated 6 according to Irwin's theory for plane stress conditions as a conservative estimate and included in Tab. S1 and S2: In most cases the plastic zone size is much smaller compared to the dimensions of the samples proving  In the case of the low deformed wires the plastic zone size became comparable to the crack length, however, the additional CTODi-measurements confirmed the presence of small scale yielding conditions.

Supplementary Table S3
Fracture toughness for the crack growth direction perpendicular to the drawing axis in terms of CTODi